{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T02:26:57Z","timestamp":1771468017551,"version":"3.50.1"},"reference-count":27,"publisher":"IOP Publishing","issue":"12","license":[{"start":{"date-parts":[[2020,11,9]],"date-time":"2020-11-09T00:00:00Z","timestamp":1604880000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/publishingsupport.iopscience.iop.org\/iop-standard\/v1"},{"start":{"date-parts":[[2020,11,9]],"date-time":"2020-11-09T00:00:00Z","timestamp":1604880000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","award":["PTDC\/MAT-PUR\/28686\/2017 UTAP-EXPL\/MAT\/0017\/2017"],"award-info":[{"award-number":["PTDC\/MAT-PUR\/28686\/2017 UTAP-EXPL\/MAT\/0017\/2017"]}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Nonlinearity"],"published-print":{"date-parts":[[2020,12,1]]},"abstract":"Abstract<\/jats:title>\n \n We show that locally bounded solutions of the inhomogeneous Trudinger\u2019s equation\n \n \n \n <\/jats:tex-math>\n \n \n \n \u2202<\/mml:mi>\n <\/mml:mrow>\n \n t<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msub>\n \n \n |<\/mml:mo>\n u<\/mml:mi>\n \n \n |<\/mml:mo>\n <\/mml:mrow>\n \n p<\/mml:mi>\n \u2212<\/mml:mo>\n 2<\/mml:mn>\n <\/mml:mrow>\n <\/mml:msup>\n u<\/mml:mi>\n <\/mml:mrow>\n <\/mml:mfenced>\n \u2212<\/mml:mo>\n d<\/mml:mi>\n i<\/mml:mi>\n v<\/mml:mi>\n |<\/mml:mo>\n \u2207<\/mml:mo>\n u<\/mml:mi>\n \n \n |<\/mml:mo>\n <\/mml:mrow>\n \n p<\/mml:mi>\n \u2212<\/mml:mo>\n 2<\/mml:mn>\n <\/mml:mrow>\n <\/mml:msup>\n \u2207<\/mml:mo>\n u<\/mml:mi>\n =<\/mml:mo>\n f<\/mml:mi>\n \u2208<\/mml:mo>\n \n \n L<\/mml:mi>\n <\/mml:mrow>\n \n q<\/mml:mi>\n ,<\/mml:mo>\n r<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msup>\n ,<\/mml:mo>\n p<\/mml:mi>\n ><\/mml:mo>\n 2<\/mml:mn>\n ,<\/mml:mo>\n <\/mml:math>\n <\/jats:inline-formula>\n are locally H\u00f6lder continuous with exponent\n \n \n \n <\/jats:tex-math>\n \n \u03b3<\/mml:mi>\n =<\/mml:mo>\n min<\/mml:mi>\n \n \n \n \n \u03b1<\/mml:mi>\n <\/mml:mrow>\n \n 0<\/mml:mn>\n <\/mml:mrow>\n \n \u2212<\/mml:mo>\n <\/mml:mrow>\n <\/mml:msubsup>\n ,<\/mml:mo>\n \n \n \n (<\/mml:mo>\n \n p<\/mml:mi>\n q<\/mml:mi>\n \u2212<\/mml:mo>\n n<\/mml:mi>\n <\/mml:mrow>\n )<\/mml:mo>\n <\/mml:mrow>\n r<\/mml:mi>\n \u2212<\/mml:mo>\n p<\/mml:mi>\n q<\/mml:mi>\n <\/mml:mrow>\n \n q<\/mml:mi>\n \n (<\/mml:mo>\n \n p<\/mml:mi>\n \u2212<\/mml:mo>\n 1<\/mml:mn>\n <\/mml:mrow>\n )<\/mml:mo>\n <\/mml:mrow>\n r<\/mml:mi>\n <\/mml:mrow>\n <\/mml:mfrac>\n <\/mml:mrow>\n <\/mml:mfenced>\n ,<\/mml:mo>\n <\/mml:math>\n <\/jats:inline-formula>\n where\n \u03b1<\/jats:italic>\n 0<\/jats:sub>\n denotes the optimal H\u00f6lder exponent for solutions of the homogeneous case. We provide a streamlined proof, using the full power of the homogeneity in the equation to develop the regularity analysis in the\n p<\/jats:italic>\n -parabolic geometry, without any need of intrinsic scaling, as anticipated by Trudinger. The main difficulty in the proof is to overcome the lack of a translation invariance property.\n <\/jats:p>","DOI":"10.1088\/1361-6544\/abb03d","type":"journal-article","created":{"date-parts":[[2020,11,9]],"date-time":"2020-11-09T05:45:55Z","timestamp":1604900755000},"page":"7054-7066","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":4,"title":["Sharp H\u00f6lder regularity for the inhomogeneous Trudinger\u2019s equation"],"prefix":"10.1088","volume":"33","author":[{"given":"Nicolau M L","family":"Diehl","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5715-2588","authenticated-orcid":false,"given":"Jos\u00e9 Miguel","family":"Urbano","sequence":"additional","affiliation":[]}],"member":"266","published-online":{"date-parts":[[2020,11,9]]},"reference":[{"key":"nonabb03dbib1","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1007\/s11854-020-0081-z","type":"journal-article","article-title":"Sharp regularity for the inhomogeneous porous medium equation","volume":"140","author":"Ara\u00fajo","year":"2020","journal-title":"J. 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All rights, including for text and data mining, AI training, and similar technologies, are reserved.","name":"copyright_information","label":"Copyright Information"},{"value":"2019-09-24","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2020-08-18","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2020-11-09","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}