Integrability for solutions to some anisotropic elliptic equations

被引：23

作者：

Leonetti, Francesco ^{[1
]}

Siepe, Francesco ^{[1
]}

机构：

[1] Univ Aquila, Dipartimento Matemat Pura & Applicata, I-67100 Laquila, Italy

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2012年 / 75卷 / 05期

关键词：

Integrability; Solution; Anisotropic; Elliptic; Equation; GROWTH-CONDITIONS; REGULARITY;

D O I：

10.1016/j.na.2011.11.028

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the boundary value problem {(n)Sigma D-i=i(i)(a(i)(x, Du(x))) = 0, x is an element of Omega; u(x) = u(*)(x), x is an element of partial derivative Omega. We show that, higher integrability of the boundary datum u(*) forces solutions u to have higher integrability as well. Assumptions on a(i)(x, z) are suggested by the Euler equation of the anisotropic functional. integral(Omega)(vertical bar D(1)u|(p1) + vertical bar D(2)u|(p2) + ... + |D(n)u|(pn))dx. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：2867 / 2873

页数：7

共 11 条

[1] PARTIAL REGULARITY UNDER ANISOTROPIC (P, Q) GROWTH-CONDITIONS [J].

ACERBI, E ;

FUSCO, N .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1994, 107 (01) :46-67

[2]

Acerbi E., 1997, COMMUNICATION

[3]

[Anonymous], 1969, QUELQUES METHODES RE

[4]

[Anonymous], 1998, ATTI SEMIN MAT FIS

[5]

[Anonymous], 1966, SEMIN MATH SUPERIEUR

[6] Sharp regularity for functionals with (p, q) growth [J].

Esposito, L ;

Leonetti, F ;

Mingione, G .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2004, 204 (01) :5-55

[7] Regularity for minimizers of functionals with p-q growth [J].

Esposito, Luca ;

Leonetti, Francesco ;

Mingione, Giuseppe .

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 1999, 6 (02) :133-148

[8]

Ladyzhenskaya O.A., 1983, LINEAR QUASILINEAR E

[9]

MARCELLINI P, 1989, ARCH RATION MECH AN, V105, P267

[10]

TANG Q, 1993, ANN MAT PUR APPL, V164, P77

← 1 2 →