Boundary continuity of solutions to elliptic equations with nonstandard growth

被引：0
作者：
Teemu Lukkari
机构：
[1] Norwegian University of Science and Technology,Department of Mathematical Sciences
来源：
manuscripta mathematica | 2010年 / 132卷
关键词：
Primary 35J60; Secondary 35J25; 35B65;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We study regularity properties of weak solutions to elliptic equations involving variable growth exponents. We prove the sufficiency of a Wiener type criterion for the regularity of boundary points. This criterion is formulated in terms of the natural capacity involving the variable growth exponent. We also prove the Hölder continuity of weak solutions up to the boundary in domains with uniformly fat complements, provided that the boundary values are Hölder continuous.
引用
收藏
页码：463 / 482
页数：19
相关论文
共 19 条
  • [1] Acerbi E.(2001)Regularity results for a class of functionals with nonstandard growth Arch. Rational Mech. Anal. 156 121-140
  • [2] Mingione G.(2005)Gradient estimates for the J. Reine Angew. Math. 584 117-148
  • [3] Acerbi E.(1997)( Differ. Equ. 33 1653-1663
  • [4] Mingione G.(2004))-Laplacean system Izv. Ross. Akad. Nauk Ser. Mat. 68 3-60
  • [5] Alkhutov Y.A.(2004)The Harnack inequality and the Hölder property of solutions of nonlinear elliptic equations with a nonstandard growth condition Math. Inequal. Appl. 7 245-253
  • [6] Alkhutov Y.A.(1999)Continuity at boundary points of solutions of quasilinear elliptic equations with a nonstandard growth condition Nonlinear Anal. 36 295-318
  • [7] Krasheninnikova O.V.(1977)Maximal function on generalized Lebesgue spaces Arch. Rational Mech. Anal. 67 25-39
  • [8] Diening L.(1994)A class of De Giorgi type and Hölder continuity Acta Math. 172 137-161
  • [9] Fan X.(1991)A regularity condition at the boundary for solutions of quasilinear elliptic equations Czechoslovak Math. J. 41 592-618
  • [10] Zhao D.(1996)The Wiener test and potential estimates for quasilinear elliptic equations Comment. Math. Univ. Carolin. 37 23-42
12