{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,20]],"date-time":"2025-10-20T10:28:28Z","timestamp":1760956108524,"version":"3.40.3"},"publisher-location":"Cham","reference-count":24,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030558734"},{"type":"electronic","value":"9783030558741"}],"license":[{"start":{"date-parts":[[2020,8,22]],"date-time":"2020-08-22T00:00:00Z","timestamp":1598054400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,8,22]],"date-time":"2020-08-22T00:00:00Z","timestamp":1598054400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021]]},"DOI":"10.1007\/978-3-030-55874-1_114","type":"book-chapter","created":{"date-parts":[[2021,5,3]],"date-time":"2021-05-03T11:52:51Z","timestamp":1620042771000},"page":"1147-1155","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Higher Order Regularity Shifts for the p-Poisson Problem"],"prefix":"10.1007","author":[{"given":"Anna","family":"Kh. Balci","sequence":"first","affiliation":[]},{"given":"Lars","family":"Diening","sequence":"additional","affiliation":[]},{"given":"Markus","family":"Weimar","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,8,22]]},"reference":[{"key":"114_CR1","doi-asserted-by":"publisher","first-page":"541","DOI":"10.1016\/j.aim.2017.06.027","volume":"316","author":"DJ Ara\u00fajo","year":"2017","unstructured":"Ara\u00fajo, D.J., Teixeira, E.V., and Urbano, J.M.: A proof of the C\np\u2032-regularity conjecture in the plane. Adv. Math. 316, 541\u2013553 (2017)","journal-title":"Adv. Math."},{"issue":"2","key":"114_CR2","doi-asserted-by":"publisher","first-page":"663","DOI":"10.1007\/s00205-017-1171-7","volume":"214","author":"B Avelin","year":"2018","unstructured":"Avelin, B., Kuusi, T., and Mingione, G.: Nonlinear Calder\u00f3n-Zygmund theory in the limiting case. Arch. Rational Mech. Anal. 214(2), 663\u2013714 (2018)","journal-title":"Arch. Rational Mech. Anal."},{"key":"114_CR3","doi-asserted-by":"publisher","first-page":"590","DOI":"10.1016\/j.jde.2019.08.009","volume":"268","author":"A Kh Balci","year":"2020","unstructured":"Balci, A.Kh., Diening, L., and Weimar, M.: Higher order Calder\u00f3n-Zygmund estimates for the p-Laplace equation. J. Differential Equations 268, 590\u2013635 (2020)","journal-title":"J. Differential Equations"},{"key":"114_CR4","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1016\/j.matpur.2017.07.011","volume":"114","author":"D Breit","year":"2018","unstructured":"Breit, D., Cianchi, A., Diening, L., Kuusi, T., and Schwarzacher, S.: Pointwise Calder\u00f3n-Zygmund gradient estimates for the p-Laplace system. J. Math. Pures Appl. 114, 146\u2013190 (2018)","journal-title":"J. Math. Pures Appl."},{"issue":"2","key":"114_CR5","doi-asserted-by":"publisher","first-page":"569","DOI":"10.1007\/s00205-018-1223-7","volume":"229","author":"A Cianchi","year":"2018","unstructured":"Cianchi, A., and Maz\u2019ya, V.G.: Second-order two-sided estimates in nonlinear elliptic problems. Arch. Rational Mech. Anal. 229(2), 569\u2013599 (2018)","journal-title":"Arch. Rational Mech. Anal."},{"key":"114_CR6","doi-asserted-by":"crossref","unstructured":"Cioica-Licht, P., and Weimar, M.: On the limit regularity in Sobolev and Besov scales related to approximation theory. J. Fourier Anal. Appl. 26(1), Art. 10, 1\u201324 (2020)","DOI":"10.1007\/s00041-019-09707-8"},{"key":"114_CR7","doi-asserted-by":"crossref","unstructured":"Clop, A., Giova, R., and Passarelli di Napoli, A.: Besov regularity for solutions of p-harmonic equations. Adv. Nonlinear Anal. 8(1), 762\u2013778 (2017)","DOI":"10.1515\/anona-2017-0030"},{"key":"114_CR8","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1016\/S1874-608X(97)80008-8","volume-title":"Multiscale Wavelet Methods for Partial Differential Equations","author":"S Dahlke","year":"1997","unstructured":"Dahlke, S., Dahmen, W., and DeVore, R.: Nonlinear approximation and adaptive techniques for solving elliptic operator equations. In: Dahmen, W., Kurdila, A., and Oswald, P. (eds) Multiscale Wavelet Methods for Partial Differential Equations, pp. 237\u2013283. Academic Press, San Diego (1997)"},{"key":"114_CR9","doi-asserted-by":"publisher","first-page":"298","DOI":"10.1016\/j.na.2015.10.015","volume":"130","author":"S Dahlke","year":"2016","unstructured":"Dahlke, S., Diening, L., Hartmann, C., Scharf, B., and Weimar M.: Besov regularity of solutions to the p-Poisson equation. Nonlinear Anal. 130, 298\u2013329 (2016)","journal-title":"Nonlinear Anal."},{"key":"114_CR10","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1017\/S0962492900002816","volume":"7","author":"RA DeVore","year":"1998","unstructured":"DeVore, R.A.: Nonlinear approximation. Acta Numer. 7, 51\u2013150 (1998)","journal-title":"Acta Numer."},{"issue":"5","key":"114_CR11","doi-asserted-by":"publisher","first-page":"1107","DOI":"10.2307\/2375066","volume":"115","author":"E DiBenedetto","year":"1993","unstructured":"DiBenedetto, E., and Manfredi, J.: On the higher integrability of the gradient of weak solutions of certain degenerate elliptic systems. Amer. J. Math. 115(5), 1107\u20131134 (1993)","journal-title":"Amer. J. Math."},{"issue":"2","key":"114_CR12","doi-asserted-by":"publisher","first-page":"637","DOI":"10.1016\/j.na.2011.08.065","volume":"75","author":"L Diening","year":"2012","unstructured":"Diening, L., Kaplick\u00fd, P., and Schwarzacher, S.: BMO estimates for the p-Laplacian. Nonlinear Anal. 75(2), 637\u2013650 (2012)","journal-title":"Nonlinear Anal."},{"issue":"289","key":"114_CR13","doi-asserted-by":"publisher","first-page":"2127","DOI":"10.1090\/S0025-5718-2013-02777-9","volume":"83","author":"F Gaspoz","year":"2014","unstructured":"Gaspoz, F., and Morin, P.: Approximation classes for adaptive higher order finite element approximation. Math. Comp. 83(289), 2127\u20132160 (2014)","journal-title":"Math. Comp."},{"issue":"41","key":"114_CR14","first-page":"1","volume":"73","author":"C Hartmann","year":"2018","unstructured":"Hartmann, C., and Weimar, M.: Besov regularity of solutions to the p-Poisson equation in the vicinity of a vertex of a polygonal domain. Results Math. 73(41), 1\u201328 (2018)","journal-title":"Results Math."},{"issue":"3","key":"114_CR15","doi-asserted-by":"publisher","first-page":"293","DOI":"10.4064\/sm-75-3-293-312","volume":"75","author":"T Iwaniec","year":"1983","unstructured":"Iwaniec, T.: Projections onto gradient fields and L\np-estimates for degenerated elliptic operators. Studia Math. 75(3), 293\u2013312 (1983).","journal-title":"Studia Math."},{"issue":"1","key":"114_CR16","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1007\/s00205-012-0562-z","volume":"207","author":"T Kuusi","year":"2013","unstructured":"Kuusi, T., and Mingione, G.: Linear potentials in nonlinear potential theory. Arch. Rational Mech. Anal. 207(1), 215\u2013246 (2013)","journal-title":"Arch. Rational Mech. Anal."},{"issue":"4","key":"114_CR17","doi-asserted-by":"publisher","first-page":"929","DOI":"10.4171\/JEMS\/780","volume":"20","author":"T Kuusi","year":"2018","unstructured":"Kuusi, T., and Mingione, G.: Vectorial nonlinear potential theory. J. Eur. Math. Soc. 20(4), 929\u20131004 (2018)","journal-title":"J. Eur. Math. Soc."},{"issue":"1","key":"114_CR18","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1007\/s11854-017-0019-2","volume":"132","author":"E Lindgren","year":"2017","unstructured":"Lindgren, E., and Lindqvist, P.: Regularity of the p-Poisson equation in the plane. J. Anal. Math. 132(1), 217\u2013228 (2017)","journal-title":"J. Anal. Math."},{"key":"114_CR19","doi-asserted-by":"publisher","DOI":"10.1515\/9783110812411","volume-title":"Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations","author":"T Runst","year":"1996","unstructured":"Runst, T., and Sickel, W.: Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations. Walter de Gruyter & Co., Berlin (1996)"},{"key":"114_CR20","doi-asserted-by":"crossref","unstructured":"Triebel, H.: Theory of Function Spaces. Birkh\u00e4user, Basel (1983)","DOI":"10.1007\/978-3-0346-0416-1"},{"key":"114_CR21","doi-asserted-by":"crossref","unstructured":"Triebel, H.: Theory of Function Spaces II. Birkh\u00e4user, Basel (1992)","DOI":"10.1007\/978-3-0346-0419-2"},{"key":"114_CR22","unstructured":"Triebel, H.: Theory of Function Spaces III. Birkh\u00e4user, Basel (2006)"},{"key":"114_CR23","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1007\/BF02392316","volume":"138","author":"K Uhlenbeck","year":"1977","unstructured":"Uhlenbeck, K.: Regularity for a class of non-linear elliptic systems. Acta Math. 138, 219\u2013240 (1977)","journal-title":"Acta Math."},{"key":"114_CR24","volume-title":"On the lack of interior regularity of the p-Poisson problem with p > 2, Math","author":"M Weimar","year":"2020","unstructured":"Weimar, M.: On the lack of interior regularity of the p-Poisson problem with p\u2009>\u20092, Math. Nachr., (2020), https:\/\/arxiv.org\/abs\/1907.12805"}],"container-title":["Lecture Notes in Computational Science and Engineering","Numerical Mathematics and Advanced Applications ENUMATH 2019"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-55874-1_114","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,6,8]],"date-time":"2022-06-08T13:04:59Z","timestamp":1654693499000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-55874-1_114"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,22]]},"ISBN":["9783030558734","9783030558741"],"references-count":24,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-55874-1_114","relation":{},"ISSN":["1439-7358","2197-7100"],"issn-type":[{"type":"print","value":"1439-7358"},{"type":"electronic","value":"2197-7100"}],"subject":[],"published":{"date-parts":[[2020,8,22]]},"assertion":[{"value":"22 August 2020","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}