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Weighted W 1, p estimates for solutions of non-linear parabolic equations over non-smooth domains

2013; Wiley; Volume: 45; Issue: 4 Linguagem: Inglês

10.1112/blms/bdt011

1469-2120

Sun‐Sig Byun, Dian K. Palagachev, Seung‐Jin Ryu,

Numerical methods in inverse problems

Bulletin of the London Mathematical SocietyVolume 45, Issue 4 p. 765-778 Papers Weighted W1,p estimates for solutions of non-linear parabolic equations over non-smooth domains Sun-Sig Byun, Corresponding Author Sun-Sig Byun [email protected] Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul 151-747, South Korea[email protected]Search for more papers by this authorDian K. Palagachev, Dian K. Palagachev Dipartimento di Matematica, Politecnico di Bari, 70 125 Bari, Italy [email protected]Search for more papers by this authorSeungjin Ryu, Seungjin Ryu Department of Mathematics, University of Seoul, Seoul 130-743, South Korea [email protected]Search for more papers by this author Sun-Sig Byun, Corresponding Author Sun-Sig Byun [email protected] Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul 151-747, South Korea[email protected]Search for more papers by this authorDian K. Palagachev, Dian K. Palagachev Dipartimento di Matematica, Politecnico di Bari, 70 125 Bari, Italy [email protected]Search for more papers by this authorSeungjin Ryu, Seungjin Ryu Department of Mathematics, University of Seoul, Seoul 130-743, South Korea [email protected]Search for more papers by this author First published: 12 March 2013 https://doi.org/10.1112/blms/bdt011Citations: 18 2010 Mathematics Subject Classification 35R05 (primary), 35K55, 35B65 (secondary). S.B. was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST)(2011-0025715). D.K.P. was partially supported by the MIUR-PRIN 2009 project Metodi variazionali ed equazioni differenziali non lineari. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Abstract We are concerned with optimal regularity theory in weighted Sobolev spaces for discontinuous non-linear parabolic problems in divergence form over a non-smooth, bounded domain. Assuming smallness in BMO of the principal part of the non-linear operator and flatness in Reifenberg sense of the boundary, we establish a global weighted W1,p estimate for the weak solutions of such problems by proving that the spatial gradient and the non-homogeneous term belong to the same weighted Lebesgue space. The result is new in the settings of non-linear parabolic problems. Citing Literature Volume45, Issue4August 2013Pages 765-778 RelatedInformation