Anisotropic elliptic equations with general growth in the gradient and Hardy-type potentials

被引：14

作者：

Della Pietra, Francesco ^{[1
]}

Gavitone, Nunzia ^{[2
]}

机构：

[1] Univ Molise, Dipartimento Biosci & Terr, Div Fis Informat & Matemat, I-86039 Termoli, CB, Italy

[2] Univ Naples Federico II, Dipartimento Matemat & Applicaz R Caccioppoli, I-80126 Naples, Italy

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2013年 / 255卷 / 11期

关键词：

Nonlinear elliptic boundary value problems; Hardy inequalities; A priori estimates; Convex symmetrization; LAPLACE EIGENVALUE PROBLEM; NATURAL GROWTH; EXISTENCE; SYMMETRIZATION; TERM;

D O I：

10.1016/j.jde.2013.07.019

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we give existence and regularity results for the solutions of problems whose prototype is { -Qv = beta(vertical bar v vertical bar)H(Dv)(q) + lambda/H-o(x)(p) vertical bar v vertical bar(p-2)v + f(x) in Omega, v = 0 on partial derivative Omega, with Omega bounded domain of R-N, N >= 2, 0 < p - 1 < q <= p < N, beta is a nonnegative continuous function and lambda >= 0. Moreover, H is a general norm of R-N, H-0 is its polar and Qv := Sigma(N)(i=1) partial derivative/partial derivative x(i)(H(Dv)Hp-1 xi(i)(Dv)). (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：3788 / 3810

页数：23

共 44 条

[1] Some remarks on elliptic problems with critical growth in the gradient [J].