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
Abdellaoui, B
Dall'Aglio, A
Peral, I
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 222 (01) : 21 - 62
[2] Abdellaoui B., 2007, ANN SC NORM SUPE S 5, VVI, P1
[3] Elliptic problems with a Hardy potential and critical growth in the gradient: Non-resonance and blow-up results
Abdellaoui, Boumediene
Peral, Ireneo
Primo, Ana
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2007, 239 (02) : 386 - 416
[4] Convex symmetrization and applications
Alvino, A
Ferone, V
Trombetti, G
Lions, PL
[J]. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1997, 14 (02): : 275 - 293
[5] Alvino A., 1977, B UNIONE MAT ITAL, V14, P148
[6] A NOTION OF TOTAL VARIATION DEPENDING ON A METRIC WITH DISCONTINUOUS COEFFICIENTS
AMAR, M
BELLETTINI, G
[J]. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1994, 11 (01): : 91 - 133
[7] Belloni M, 2006, J EUR MATH SOC, V8, P123
[8] Isoperimetric inequalities, Wulff shape and related questions for strongly nonlinear elliptic operators
Belloni, M
Ferone, V
Kawohl, B
[J]. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2003, 54 (05): : 771 - 783
[9] Benilan P., 1995, ANN SCUOLA NORM-SCI, V22, P241
[10] Bennett C., 1988, PURE APPL MATH, V129

← 1 2 3 4 5 →