Second-Order Two-Sided Estimates in Nonlinear Elliptic Problems

被引：65

作者：

Cianchi, Andrea ^{[1
]}

Maz'ya, Vladimir G. ^{[2
,3
]}

机构：

[1] Univ Firenze, Dipartimento Matemat & Informat U Dini, Viale Morgagni 67-A, I-50134 Florence, Italy

[2] Linkoping Univ, Dept Math, S-58183 Linkoping, Sweden

[3] RUDN Univ, 6 Miklukho Maklay St, Moscow 117198, Russia

来源：

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2018年 / 229卷 / 02期

关键词：

GENERAL GROWTH; WEAK SOLUTIONS; VARIATIONAL-PROBLEMS; REGULARITY; EQUATIONS; GRADIENT; BOUNDEDNESS; BOUNDARY;

D O I：

10.1007/s00205-018-1223-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Best possible second-order regularity is established for solutions to p-Laplacian type equations with and a square-integrable right-hand side. Our results provide a nonlinear counterpart of the classical L (2)-coercivity theory for linear problems, which is missing in the existing literature. Both local and global estimates are obtained. The latter apply to solutions to either Dirichlet or Neumann boundary value problems. Minimal regularity on the boundary of the domain is required, although our conclusions are new even for smooth domains. If the domain is convex, no regularity of its boundary is needed at all.

引用

页码：569 / 599

页数：31

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