Multivalued problem with Robin boundary condition involving diffuse measure data and variable exponent

被引：13

作者：

Ouaro, Stanislas ^{[1
]}

Ouedraogo, Arouna ^{[1
]}

Soma, Safimba ^{[1
]}

机构：

[1] Univ Ouagadougou, Dept Math, LAME, Unite Format & Rech Sci Exactes & Appl, Ouagadougou, Burkina Faso

来源：

ADVANCES IN NONLINEAR ANALYSIS | 2014年 / 3卷 / 04期

关键词：

Robin boundary condition; diffuse measure; Biting Lemma of Chacon; maximal monotone graph; Radon measure data; weak solution; entropic solution; Leray-Lions operator; subdifferential operator; EXISTENCE;

D O I：

10.1515/anona-2014-0010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study a nonlinear elliptic problem with Robin type boundary condition, governed by a general Leray-Lions operator with variable exponents and diffuse Radon measure data which does not charge the sets of zero p(.)-capacity. We prove an existence and uniqueness result of a weak solution.

引用

页码：209 / 235

页数：27

共 16 条

[1]

Andreu F., 1997, Adv. Math. Sci. Appl., V7, P183

[2]

[Anonymous], 1995, ANN SCUOLA NORM-SCI

[3]

[Anonymous], 1973, Operateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert

[4] Existence and uniqueness of entropy solutions for nonlinear elliptic equations with measure data [J].

Boccardo, L ;

Gallouet, T ;

Orsina, L .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1996, 13 (05) :539-551

[5]

Bonzi BK, 2012, ELECTRON J DIFFER EQ

[6]

Brezis H., 1983, Analyse fonctionnelle, Theorie et applications

[7] CONTINUITY AND COMPACTNESS OF MEASURES [J].

BROOKS, JK ;

CHACON, RV .

ADVANCES IN MATHEMATICS, 1980, 37 (01) :16-26

[8] Lebesgue and Sobolev Spaces with Variable Exponents [J].

Diening, Lars ;

Harjulehto, Petteri ;

Hasto, Peter ;

Ruzicka, Michael .

LEBESGUE AND SOBOLEV SPACES WITH VARIABLE EXPONENTS, 2011, 2017 :1-+

[9] On the spaces Lp(x)(Ω) and Wm, p(x)(Ω) [J].

Fan, XL ;

Zhao, D .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2001, 263 (02) :424-446

[10]

KOVACIK O, 1991, CZECH MATH J, V41, P592

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