On the relation between generalized Morrey spaces and measure data problems

被引：4

作者：

Baroni, Paolo ^{[1
]}

机构：

[1] Univ Parma, Dept Math Phys & Comp Sci, I-43124 Parma, Italy

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2018年 / 177卷

关键词：

Measure data; Generalized Morrey space; Marcinkiewicz space; NONLINEAR POTENTIAL-THEORY; DEGENERATE PARABOLIC EQUATIONS; ELLIPTIC PROBLEMS; ZYGMUND THEORY;

D O I：

10.1016/j.na.2018.06.011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider measure data problems of p-Laplacian type. The measure on the right-hand side has the property that the total variation of a generic ball decays in terms of generic functions of the radius; we show that this condition has a natural relation with gradient integrability properties and we get, as corollary, borderline cases of classic results. (C) 2018 Elsevier Ltd. All rights reserved.

引用

页码：24 / 45

页数：22

共 28 条

[1]

Adams D.R., 1996, GRUNDLEHREN MATH WIS, V314

[2]

[Anonymous], 2003, DIRECT METHODS CALCU, DOI DOI 10.1142/5002

[3] Nonlinear Caldern-Zygmund Theory in the Limiting Case [J].

Avelin, Benny ;

Kuusi, Tuomo ;

Mingione, Giuseppe .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2018, 227 (02) :663-714

[4] Singular parabolic equations, measures satisfying density conditions, and gradient integrability [J].

Baroni, Paolo .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2017, 153 :89-116

[5] Marcinkiewicz estimates for degenerate parabolic equations with measure data [J].

Baroni, Paolo .

JOURNAL OF FUNCTIONAL ANALYSIS, 2014, 267 (09) :3397-3426

[6] Global estimates for nonlinear parabolic equations [J].

Baroni, Paolo ;

Di Castro, Agnese ;

Palatucci, Giampiero .

JOURNAL OF EVOLUTION EQUATIONS, 2013, 13 (01) :163-195

[7]

Baroni P, 2012, HOUSTON J MATH, V38, P855

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

BOCCARDO, L ;

GALLOUET, T .

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

[9]

Cianchi A, 2004, REV MAT IBEROAM, V20, P427

[10]

Cianchi A., PREPRINT

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