Riesz and Wolff potentials and elliptic equations in variable exponent weak Lebesgue spaces

被引：25

作者：

Almeida, A. ^{[1
]}

Harjulehto, P. ^{[2
]}

Hasto, P. ^{[3
]}

Lukkari, T. ^{[4
]}

机构：

[1] Univ Aveiro, Dept Math, Ctr Res & Dev Math & Applicat, P-3810193 Aveiro, Portugal

[2] Univ Turku, Dept Math & Stat, Turku 20014, Finland

[3] Univ Oulu, Dept Math Sci, POB 3000, Oulu 90014, Finland

[4] Univ Jyvaskyla, Dept Math & Stat, Jyvaskyla 40014, Finland

来源：

ANNALI DI MATEMATICA PURA ED APPLICATA | 2015年 / 194卷 / 02期

基金：

芬兰科学院;

关键词：

Variable exponent; Weak Lebesgue space; Real interpolation; Riesz potential; Wolff potential; Non-standard growth condition; Integrability of solutions; Integrability estimates; NONSTANDARD GROWTH; SOBOLEV SPACES; INTERPOLATION;

D O I：

10.1007/s10231-013-0382-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove optimal integrability results for solutions of the p(.)-Laplace equation in the scale of (weak) Lebesgue spaces. To obtain this, we show that variable exponent Riesz and Wolff potentials map L-1 to variable exponent weak Lebesgue spaces.

引用

页码：405 / 424

页数：20

共 30 条

[1] Regularity results for a class of functionals with non-standard growth [J].

Acerbi, E ;

Mingione, G .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2001, 156 (02) :121-140

[2] Interpolation in variable exponent spaces [J].

Almeida, Alexandre ;

Hasto, Peter .

REVISTA MATEMATICA COMPLUTENSE, 2014, 27 (02) :657-676

[3] Real Interpolation of Generalized Besov-Hardy Spaces and Applications [J].

Almeida, Alexandre ;

Caetano, Antonio .

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2011, 17 (04) :691-719

[4]

[Anonymous], 1978, INTERPOLATION THEORY

[5]

BOCCARDO L, 1992, COMMUN PART DIFF EQ, V17, P641

[6] NON-LINEAR ELLIPTIC AND PARABOLIC EQUATIONS INVOLVING MEASURE DATA [J].

BOCCARDO, L ;

GALLOUET, T .

JOURNAL OF FUNCTIONAL ANALYSIS, 1989, 87 (01) :149-169

[7] GRADIENT ESTIMATES VIA NON STANDARD POTENTIALS AND CONTINUITY [J].

Boegelein, Verena ;

Habermann, Jens .

ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 2010, 35 (02) :641-678

[8]

Brudnyi Y., 1991, INTERPOLATION FUNCTO, V1

[9] Riesz potential and Sobolev embeddings on generalized Lebesgue and Sobolev spaces Lp(•) and Wk,p [J].

Diening, L .

MATHEMATISCHE NACHRICHTEN, 2004, 268 :31-43

[10]

Diening L., 2004, FSDONA04 P, P38

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