{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,3]],"date-time":"2025-07-03T04:14:16Z","timestamp":1751516056198,"version":"3.41.0"},"reference-count":53,"publisher":"Walter de Gruyter GmbH","issue":"3","funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/00013\/2020 and UIDP\/00013\/2020"],"award-info":[{"award-number":["UIDB\/00013\/2020 and UIDP\/00013\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000893","name":"Simons Foundation","doi-asserted-by":"publisher","award":["1160640"],"award-info":[{"award-number":["1160640"]}],"id":[{"id":"10.13039\/100000893","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,7,1]]},"abstract":"Abstract<\/jats:title>\n In this work we prove that the non-negative functions \n \n \n \n u<\/m:mi>\n \u2208<\/m:mo>\n \n \n L<\/m:mi>\n loc<\/m:mi>\n s<\/m:mi>\n <\/m:msubsup>\n \u2062<\/m:mo>\n \n (<\/m:mo>\n \u03a9<\/m:mi>\n )<\/m:mo>\n <\/m:mrow>\n <\/m:mrow>\n <\/m:mrow>\n <\/m:math>\n \n {u\\in L^{s}_{\\rm loc}(\\Omega)}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>, for some \n \n \n \n s<\/m:mi>\n ><\/m:mo>\n 0<\/m:mn>\n <\/m:mrow>\n <\/m:math>\n \n {s>0}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>, belonging to the De Giorgi classes<\/jats:p>\n \n \n \n \n \n \n \u2a0d<\/m:mo>\n \n \n B<\/m:mi>\n \n r<\/m:mi>\n \u2062<\/m:mo>\n \n (<\/m:mo>\n \n 1<\/m:mn>\n -<\/m:mo>\n \u03c3<\/m:mi>\n <\/m:mrow>\n )<\/m:mo>\n <\/m:mrow>\n <\/m:mrow>\n <\/m:msub>\n \u2062<\/m:mo>\n \n (<\/m:mo>\n \n x<\/m:mi>\n 0<\/m:mn>\n <\/m:msub>\n )<\/m:mo>\n <\/m:mrow>\n <\/m:mrow>\n <\/m:msub>\n |<\/m:mo>\n \u2207<\/m:mo>\n \n \n (<\/m:mo>\n u<\/m:mi>\n -<\/m:mo>\n k<\/m:mi>\n )<\/m:mo>\n <\/m:mrow>\n -<\/m:mo>\n <\/m:msub>\n \n \n |<\/m:mo>\n p<\/m:mi>\n <\/m:msup>\n <\/m:mpadded>\n d<\/m:mi>\n x<\/m:mi>\n \u2a7d<\/m:mo>\n \n \n c<\/m:mi>\n \n \u03c3<\/m:mi>\n q<\/m:mi>\n <\/m:msup>\n <\/m:mfrac>\n <\/m:mpadded>\n \u039b<\/m:mi>\n \n (<\/m:mo>\n \n x<\/m:mi>\n 0<\/m:mn>\n <\/m:msub>\n ,<\/m:mo>\n r<\/m:mi>\n ,<\/m:mo>\n k<\/m:mi>\n )<\/m:mo>\n <\/m:mrow>\n \n \n (<\/m:mo>\n \n k<\/m:mi>\n r<\/m:mi>\n <\/m:mfrac>\n )<\/m:mo>\n <\/m:mrow>\n p<\/m:mi>\n <\/m:msup>\n \n \n (<\/m:mo>\n \n \n |<\/m:mo>\n \n B<\/m:mi>\n r<\/m:mi>\n <\/m:msub>\n \n (<\/m:mo>\n \n x<\/m:mi>\n 0<\/m:mn>\n <\/m:msub>\n )<\/m:mo>\n <\/m:mrow>\n \u2229<\/m:mo>\n \n {<\/m:mo>\n u<\/m:mi>\n \u2a7d<\/m:mo>\n k<\/m:mi>\n }<\/m:mo>\n <\/m:mrow>\n |<\/m:mo>\n <\/m:mrow>\n \n |<\/m:mo>\n \n \n B<\/m:mi>\n r<\/m:mi>\n <\/m:msub>\n \u2062<\/m:mo>\n \n (<\/m:mo>\n \n x<\/m:mi>\n 0<\/m:mn>\n <\/m:msub>\n )<\/m:mo>\n <\/m:mrow>\n <\/m:mrow>\n |<\/m:mo>\n <\/m:mrow>\n <\/m:mfrac>\n )<\/m:mo>\n <\/m:mrow>\n \n 1<\/m:mn>\n -<\/m:mo>\n \u03b4<\/m:mi>\n <\/m:mrow>\n <\/m:msup>\n ,<\/m:mo>\n <\/m:mrow>\n <\/m:math>\n \n \\barint_{B_{r(1-\\sigma)}(x_{0})}|\\nabla(u-k)_{-}|^{p}\\,dx\\leqslant\\frac{c}{%\n\\sigma^{q}}\\,\\Lambda(x_{0},r,k)\\bigg{(}\\frac{k}{r}\\bigg{)}^{p}\\bigg{(}\\frac{|B%\n_{r}(x_{0})\\cap\\{u\\leqslant k\\}|}{|B_{r}(x_{0})|}\\bigg{)}^{1-\\delta},<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:disp-formula>\n <\/jats:p>\n under proper assumptions on \u039b, satisfy a weak Harnack inequality with a constant depending on the \n \n \n \n L<\/m:mi>\n s<\/m:mi>\n <\/m:msup>\n <\/m:math>\n \n {L^{s}}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>-norm of u<\/jats:italic>. Under suitable assumptions on \u039b, the minimizers of elliptic functionals with generalized Orlicz growth belong to De Giorgi classes satisfying the above condition; thus this study gives a wider interpretation of Harnack-type estimates derived to double-phase, degenerate double-phase functionals and functionals with variable exponents.<\/jats:p>","DOI":"10.1515\/acv-2024-0032","type":"journal-article","created":{"date-parts":[[2024,11,19]],"date-time":"2024-11-19T17:34:17Z","timestamp":1732037657000},"page":"639-652","source":"Crossref","is-referenced-by-count":0,"title":["The weak Harnack inequality for unbounded minimizers of elliptic functionals with generalized Orlicz growth"],"prefix":"10.1515","volume":"18","author":[{"given":"Simone","family":"Ciani","sequence":"first","affiliation":[{"name":"Department of Mathematics , University of Bologna , Piazza Porta San Donato 5, 40126 Bologna , Italy"}]},{"given":"Eurica","family":"Henriques","sequence":"additional","affiliation":[{"name":"Centro de Matem\u00e1tica, Universidade do Minho \u2013 Polo CMAT-UTAD, Braga ; and Departamento de Matem\u00e1tica , 386363 Universidade de Tr\u00e1s-os-Montes e Alto Douro , 5000-801 Vila Real , Portugal"}]},{"given":"Igor I.","family":"Skrypnik","sequence":"additional","affiliation":[{"name":"Institute of Applied Mathematics and Mechanics , National Academy of Sciences of Ukraine , Batiouk Str. 19, 84116 Sloviansk ; and Vasyl\u2019 Stus Donetsk National University, 600-richcha Str. 21, 21021 Vinnytsia , Ukraine"}]}],"member":"374","published-online":{"date-parts":[[2024,11,17]]},"reference":[{"key":"#cr-split#-2025070217280550534_j_acv-2024-0032_ref_001.1","unstructured":"Y. A. Alkhutov, The Harnack inequality and the H\u00f6lder property of solutions of nonlinear elliptic equations with a nonstandard growth condition (in Russian), Differ. Uravn. 33 (1997), no. 12, 1651-1660"},{"key":"#cr-split#-2025070217280550534_j_acv-2024-0032_ref_001.2","unstructured":"translation in Differential Equations 33 (1997), no. 12, 1653-1663."},{"key":"#cr-split#-2025070217280550534_j_acv-2024-0032_ref_002.1","doi-asserted-by":"crossref","unstructured":"Y. A. Alkhutov and O. V. Krasheninnikova, On the continuity of solutions of elliptic equations with a variable order of nonlinearity (in Russian, Tr. Mat. Inst. Steklova 261 (2008), 7-15","DOI":"10.1134\/S0081543808020016"},{"key":"#cr-split#-2025070217280550534_j_acv-2024-0032_ref_002.2","unstructured":"translation in Proc. Steklov Inst. Math. 261 (2008), 1-10."},{"key":"2025070217280550534_j_acv-2024-0032_ref_003","doi-asserted-by":"crossref","unstructured":"Y. A. Alkhutov and M. D. Surnachev,\nA Harnack inequality for a transmission problem with\n \n \n \n p\n \u2062\n \n (\n x\n )\n \n \n \n \n p(x)\n \n -Laplacian,\nAppl. Anal. 98 (2019), no. 1\u20132, 332\u2013344.","DOI":"10.1080\/00036811.2017.1423473"},{"key":"2025070217280550534_j_acv-2024-0032_ref_004","doi-asserted-by":"crossref","unstructured":"Y. A. Alkhutov and M. D. Surnachev,\nHarnack\u2019s inequality for the \n \n \n \n p\n \u2062\n \n (\n x\n )\n \n \n \n \n p(x)\n \n -Laplacian with a two-phase exponent \n \n \n \n p\n \u2062\n \n (\n x\n )\n \n \n \n \n p(x)\n \n ,\nJ. Math. Sci. (N.\u2009Y.) 244 (2020), no. 2, 116\u2013147.","DOI":"10.1007\/s10958-019-04609-y"},{"key":"2025070217280550534_j_acv-2024-0032_ref_005","doi-asserted-by":"crossref","unstructured":"Y. A. Alkhutov and M. D. Surnachev,\nH\u00f6lder continuity and Harnack\u2019s inequality for \n \n \n \n p\n \u2062\n \n (\n x\n )\n \n \n \n \n p(x)\n \n -harmonic functions,\nTr. Mat. Inst. Steklova 308 (2020), 7\u201327.","DOI":"10.1134\/S0081543820010010"},{"key":"2025070217280550534_j_acv-2024-0032_ref_006","doi-asserted-by":"crossref","unstructured":"W. Arriagada and J. Huentutripay,\nA Harnack inequality in Orlicz\u2013Sobolev spaces,\nStudia Math. 243 (2018), no. 2, 117\u2013137.","DOI":"10.4064\/sm8764-9-2017"},{"key":"2025070217280550534_j_acv-2024-0032_ref_007","doi-asserted-by":"crossref","unstructured":"P. Baroni, M. Colombo and G. Mingione,\nHarnack inequalities for double phase functionals,\nNonlinear Anal. 121 (2015), 206\u2013222.","DOI":"10.1016\/j.na.2014.11.001"},{"key":"2025070217280550534_j_acv-2024-0032_ref_008","doi-asserted-by":"crossref","unstructured":"P. Baroni, M. Colombo and G. Mingione,\nNonautonomous functionals, borderline cases and related function classes,\nSt. Petersburg Math. J. 27 (2016), 347\u2013379.","DOI":"10.1090\/spmj\/1392"},{"key":"2025070217280550534_j_acv-2024-0032_ref_009","doi-asserted-by":"crossref","unstructured":"P. Baroni, M. Colombo and G. Mingione,\nRegularity for general functionals with double phase,\nCalc. Var. Partial Differential Equations 57 (2018), no. 2, Paper No. 62.","DOI":"10.1007\/s00526-018-1332-z"},{"key":"2025070217280550534_j_acv-2024-0032_ref_010","doi-asserted-by":"crossref","unstructured":"P. Bella and M. Sch\u00e4ffner,\nLocal boundedness and Harnack inequality for solutions of linear nonuniformly elliptic equations,\nComm. Pure Appl. Math. 74 (2021), no. 3, 453\u2013477.","DOI":"10.1002\/cpa.21876"},{"key":"2025070217280550534_j_acv-2024-0032_ref_011","doi-asserted-by":"crossref","unstructured":"A. Benyaiche, P. Harjulehto, P. H\u00e4st\u00f6 and A. Karppinen,\nThe weak Harnack inequality for unbounded supersolutions of equations with generalized Orlicz growth,\nJ. Differential Equations 275 (2021), 790\u2013814.","DOI":"10.1016\/j.jde.2020.11.007"},{"key":"2025070217280550534_j_acv-2024-0032_ref_012","doi-asserted-by":"crossref","unstructured":"E. Bombieri and E. Giusti,\nHarnack\u2019s inequality for elliptic differential equations on minimal surfaces,\nInvent. Math. 15 (1972), 24\u201346.","DOI":"10.1007\/BF01418640"},{"key":"2025070217280550534_j_acv-2024-0032_ref_013","doi-asserted-by":"crossref","unstructured":"K. O. Buryachenko and I. I. Skrypnik,\nLocal continuity and Harnack\u2019s inequality for double-phase parabolic equations,\nPotential Anal. 56 (2022), no. 1, 137\u2013164.","DOI":"10.1007\/s11118-020-09879-9"},{"key":"2025070217280550534_j_acv-2024-0032_ref_014","doi-asserted-by":"crossref","unstructured":"M. Colombo and G. Mingione,\nBounded minimisers of double phase variational integrals,\nArch. Ration. Mech. Anal. 218 (2015), no. 1, 219\u2013273.","DOI":"10.1007\/s00205-015-0859-9"},{"key":"2025070217280550534_j_acv-2024-0032_ref_015","doi-asserted-by":"crossref","unstructured":"M. Colombo and G. Mingione,\nRegularity for double phase variational problems,\nArch. Ration. Mech. Anal. 215 (2015), no. 2, 443\u2013496.","DOI":"10.1007\/s00205-014-0785-2"},{"key":"2025070217280550534_j_acv-2024-0032_ref_016","doi-asserted-by":"crossref","unstructured":"M. Colombo and G. Mingione,\nCalder\u00f3n\u2013Zygmund estimates and non-uniformly elliptic operators,\nJ. Funct. Anal. 270 (2016), no. 4, 1416\u20131478.","DOI":"10.1016\/j.jfa.2015.06.022"},{"key":"2025070217280550534_j_acv-2024-0032_ref_017","unstructured":"E. De Giorgi,\nSulla differenziabilit\u00e0 e l\u2019analiticit\u00e0 delle estremali degli integrali multipli regolari,\nMem. Accad. Sci. Torino. Cl. Sci. Fis. Mat. Nat. (3) 3 (1957), 25\u201343."},{"key":"2025070217280550534_j_acv-2024-0032_ref_018","doi-asserted-by":"crossref","unstructured":"E. DiBenedetto, U. Gianazza and V. Vespri,\nLocal clustering of the non-zero set of functions in \n \n \n \n \n W\n \n 1\n ,\n 1\n \n \n \u2062\n \n (\n E\n )\n \n \n \n \n W^{1,1}(E)\n \n ,\nAtti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 17 (2006), no. 3, 223\u2013225.","DOI":"10.4171\/rlm\/465"},{"key":"2025070217280550534_j_acv-2024-0032_ref_019","doi-asserted-by":"crossref","unstructured":"E. DiBenedetto and N. S. Trudinger,\nHarnack inequalities for quasiminima of variational integrals,\nAnn. Inst. H. Poincar\u00e9 Anal. Non Lin\u00e9aire 1 (1984), no. 4, 295\u2013308.","DOI":"10.1016\/s0294-1449(16)30424-3"},{"key":"2025070217280550534_j_acv-2024-0032_ref_020","unstructured":"X. Fan,\nA Class of De Giorgi Type and H\u00f6lder Continuity of Minimizers of Variational with \n \n \n \n \n m\n \u2062\n \n (\n x\n )\n \n \n \n \n m(x)\n \n \n -Growth Condition,\nLanzhou University, Lanzhou, 1995."},{"key":"2025070217280550534_j_acv-2024-0032_ref_021","doi-asserted-by":"crossref","unstructured":"X. Fan and D. Zhao,\nA class of De Giorgi type and H\u00f6lder continuity,\nNonlinear Anal. 36 (1999), no. 3, 295\u2013318.","DOI":"10.1016\/S0362-546X(97)00628-7"},{"key":"2025070217280550534_j_acv-2024-0032_ref_022","doi-asserted-by":"crossref","unstructured":"O. V. Hadzhy, I. I. Skrypnik and M. V. Voitovych,\nInterior continuity, continuity up to the boundary, and Harnack\u2019s inequality for double-phase elliptic equations with nonlogarithmic conditions,\nMath. Nachr. 296 (2023), no. 9, 3892\u20133914.","DOI":"10.1002\/mana.202000574"},{"key":"2025070217280550534_j_acv-2024-0032_ref_023","doi-asserted-by":"crossref","unstructured":"P. Harjulehto and P. H\u00e4st\u00f6,\nBoundary regularity under generalized growth conditions,\nZ. Anal. Anwend. 38 (2019), no. 1, 73\u201396.","DOI":"10.4171\/zaa\/1628"},{"key":"2025070217280550534_j_acv-2024-0032_ref_024","doi-asserted-by":"crossref","unstructured":"P. Harjulehto, P. H\u00e4st\u00f6 and M. Lee,\nH\u00f6lder continuity of \u03c9-minimizers of functionals with generalized Orlicz growth,\nAnn. Sc. Norm. Super. Pisa Cl. Sci. (5) 22 (2021), no. 2, 549\u2013582.","DOI":"10.2422\/2036-2145.201908_015"},{"key":"2025070217280550534_j_acv-2024-0032_ref_025","doi-asserted-by":"crossref","unstructured":"P. Harjulehto, P. H\u00e4st\u00f6 and O. Toivanen,\nH\u00f6lder regularity of quasiminimizers under generalized growth conditions,\nCalc. Var. Partial Differential Equations 56 (2017), no. 2, Paper No. 22.","DOI":"10.1007\/s00526-017-1114-z"},{"key":"2025070217280550534_j_acv-2024-0032_ref_026","doi-asserted-by":"crossref","unstructured":"P. Harjulehto, J. Kinnunen and T. Lukkari,\nUnbounded supersolutions of nonlinear equations with nonstandard growth,\nBound. Value Probl. 2007 (2007), Article ID 48348.","DOI":"10.1155\/2007\/48348"},{"key":"2025070217280550534_j_acv-2024-0032_ref_027","doi-asserted-by":"crossref","unstructured":"P. Harjulehto, T. Kuusi, T. Lukkari, N. Marola and M. Parviainen,\nHarnack\u2019s inequality for quasiminimizers with nonstandard growth conditions,\nJ. Math. Anal. Appl. 344 (2008), no. 1, 504\u2013520.","DOI":"10.1016\/j.jmaa.2008.03.018"},{"key":"2025070217280550534_j_acv-2024-0032_ref_028","doi-asserted-by":"crossref","unstructured":"P. H\u00e4st\u00f6 and J. Ok,\nRegularity theory for non-autonomous problems with a priori assumptions,\nCalc. Var. Partial Differential Equations 62 (2023), no. 9, Paper No. 251.","DOI":"10.1007\/s00526-023-02587-3"},{"key":"2025070217280550534_j_acv-2024-0032_ref_029","unstructured":"O. A. Ladyzhenskaya and N. N. Ural\u2019tseva,\nLinear and Quasilinear Elliptic Equations,\nNauka, Moscow, 1973."},{"key":"2025070217280550534_j_acv-2024-0032_ref_030","doi-asserted-by":"crossref","unstructured":"G. M. Lieberman,\nThe natural generalization of the natural conditions of Ladyzhenskaya and Ural\u2019tseva for elliptic equations,\nComm. Partial Differential Equations 16 (1991), no. 2\u20133, 311\u2013361.","DOI":"10.1080\/03605309108820761"},{"key":"2025070217280550534_j_acv-2024-0032_ref_031","doi-asserted-by":"crossref","unstructured":"V. Liskevich and I. I. Skrypnik,\nHarnack inequality and continuity of solutions to elliptic equations with nonstandard growth conditions and lower order terms,\nAnn. Mat. Pura Appl. (4) 189 (2010), no. 2, 333\u2013356.","DOI":"10.1007\/s10231-009-0111-z"},{"key":"2025070217280550534_j_acv-2024-0032_ref_032","doi-asserted-by":"crossref","unstructured":"P. Marcellini,\nRegularity of minimizers of integrals of the calculus of variations with nonstandard growth conditions,\nArch. Ration. Mech. Anal. 105 (1989), no. 3, 267\u2013284.","DOI":"10.1007\/BF00251503"},{"key":"2025070217280550534_j_acv-2024-0032_ref_033","doi-asserted-by":"crossref","unstructured":"P. Marcellini,\nRegularity and existence of solutions of elliptic equations with \n \n \n \n p\n ,\n q\n \n \n \n p,q\n \n -growth conditions,\nJ. Differential Equations 90 (1991), no. 1, 1\u201330.","DOI":"10.1016\/0022-0396(91)90158-6"},{"key":"2025070217280550534_j_acv-2024-0032_ref_034","doi-asserted-by":"crossref","unstructured":"Y. Mizuta, T. Ohno and T. Shimomura,\nSobolev\u2019s theorem for double phase functionals,\nMath. Inequal. Appl. 23 (2020), no. 1, 17\u201333.","DOI":"10.7153\/mia-2020-23-02"},{"key":"2025070217280550534_j_acv-2024-0032_ref_035","doi-asserted-by":"crossref","unstructured":"J. Moser,\nOn Harnack\u2019s theorem for elliptic differential equations,\nComm. Pure Appl. Math. 14 (1961), 577\u2013591.","DOI":"10.1002\/cpa.3160140329"},{"key":"2025070217280550534_j_acv-2024-0032_ref_036","doi-asserted-by":"crossref","unstructured":"J. Ok,\nRegularity for double phase problems under additional integrability assumptions,\nNonlinear Anal. 194 (2020), Article ID 111408.","DOI":"10.1016\/j.na.2018.12.019"},{"key":"2025070217280550534_j_acv-2024-0032_ref_037","doi-asserted-by":"crossref","unstructured":"M. A. Ragusa and A. Tachikawa,\nRegularity for minimizers for functionals of double phase with variable exponents,\nAdv. Nonlinear Anal. 9 (2020), no. 1, 710\u2013728.","DOI":"10.1515\/anona-2020-0022"},{"key":"2025070217280550534_j_acv-2024-0032_ref_038","unstructured":"M. A. Savchenko, I. I. Skrypnik and Y. A. Yevgenieva,\nA note on the weak Harnack inequality for unbounded minimizers of elliptic functionals with generalized Orlicz growth,\npreprint (2023), https:\/\/arxiv.org\/abs\/2304.04499."},{"key":"2025070217280550534_j_acv-2024-0032_ref_039","doi-asserted-by":"crossref","unstructured":"M. O. Savchenko, I. I. Skrypnik and Y. A. Yevgenieva,\nContinuity and Harnack inequalities for local minimizers of non-uniformly elliptic functionals with generalized Orlicz growth under the non-logarithmic conditions,\nNonlinear Anal. 230 (2023), Article ID 113221.","DOI":"10.1016\/j.na.2023.113221"},{"key":"2025070217280550534_j_acv-2024-0032_ref_040","doi-asserted-by":"crossref","unstructured":"M. A. Shan, I. I. Skrypnik and M. V. Voitovych,\nHarnack\u2019s inequality for quasilinear elliptic equations with generalized Orlicz growth,\nElectron. J. Differential Equations 2021 (2021), Paper No. 27.","DOI":"10.58997\/ejde.2021.27"},{"key":"2025070217280550534_j_acv-2024-0032_ref_041","doi-asserted-by":"crossref","unstructured":"I. Skrypnik and Y. Yevgenieva,\nHarnack inequality for solutions of the \n \n \n \n p\n \u2062\n \n (\n x\n )\n \n \n \n \n p(x)\n \n -Laplace equation under the precise non-logarithmic Zhikov\u2019s conditions,\nCalc. Var. Partial Differential Equations 63 (2024), no. 1, Paper No. 7.","DOI":"10.1007\/s00526-023-02608-1"},{"key":"2025070217280550534_j_acv-2024-0032_ref_042","doi-asserted-by":"crossref","unstructured":"I. I. Skrypnik and M. V. Voitovych,\n\n \n \n \n \u212c\n 1\n \n \n \n \\mathcal{B}_{1}\n \n classes of De Giorgi\u2013Ladyzhenskaya\u2013Ural\u2019tseva and their applications to elliptic and parabolic equations with generalized Orlicz growth conditions,\nNonlinear Anal. 202 (2021), Paper No. 112135.","DOI":"10.1016\/j.na.2020.112135"},{"key":"2025070217280550534_j_acv-2024-0032_ref_043","doi-asserted-by":"crossref","unstructured":"I. I. Skrypnik and M. V. Voitovych,\nOn the continuity of solutions of quasilinear parabolic equations with generalized Orlicz growth under non-logarithmic conditions,\nAnn. Mat. Pura Appl. 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