Global gradient estimates for degenerate parabolic equations in nonsmooth domains

被引：0

作者：

Mikko Parviainen

机构：

[1] Helsinki University of Technology,Institute of Mathematics

来源：

Annali di Matematica Pura ed Applicata | 2009年 / 188卷

关键词：

Boundary value problem; Gehring lemma; Global higher integrability; Initial value problem; Reverse Hölder inequality; 35K60; 35K55; 35K15; 49N60;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

This paper studies the global regularity theory for degenerate nonlinear parabolic partial differential equations. Our objective is to show that weak solutions belong to a higher Sobolev space than assumed a priori if the complement of the domain satisfies a capacity density condition and if the boundary values are sufficiently smooth. Moreover, we derive integrability estimates for the gradient. The results extend to the parabolic systems as well. The higher integrability estimates provide a useful tool in several applications.

引用

页码：333 / 358

页数：25

共 27 条

[1] Acerbi E.(2007)Gradient estimates for a class of parabolic systems Duke Math. J. 136 285-320
[2] Mingione G.(1986)On strong barriers and an inequality of Hardy for domains in J. Lond. Math. Soc. (2) 34 274-290
[3] Ancona A.(1992)-estimates for the gradients of solutions of initial boundary value problems to quasilinear parabolic systems (Russian) St. Petersburg State Univ., Problems Math. Anal. 13 5-18
[4] Arkhipova A.A.(1957)Generalized solutions of a system of differential equations of first order and of elliptic type with discontinuous coefficients (Russian) Mat. Sb. N.S. 43 451-503
[5] Bojarski B.V.(2004)The Calc. Var. Partial Differential Equations 20 235-256
[6] Duzaar F.(2005)-harmonic approximation and the regularity of Ann. Inst. H. Poincaré Anal. Non Linéaire 22 705-751
[7] Mingione G.(1975)-harmonic maps Duke Math. J. 42 121-136
[8] Duzaar F.(1973)Second order parabolic systems, optimal regularity, and singular sets of solutions Acta Math. 130 265-277
[9] Mingione G.(1979)Some results on regularity for solutions of non-linear elliptic systems and quasi-regular functions J. Reine Angew. Math. 311/312 145-169
[10] Elcrat A.(1982)The Math. Z. 179 437-451

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