Regularity for p-harmonic equations with right-hand side in Orlicz-Zygmund classes

被引：11

作者：

Carozza, Menita ^{[2
]}

Moscariello, Gioconda ^{[1
]}

di Napoli, Antonia Passarelli ^{[1
]}

机构：

[1] Univ Naples Federico II, Dipartimento Matemat & Applicaz, Via Cintia, I-80126 Naples, Italy

[2] Univ Sannio, Piazza Arechi 2, I-82100 Benevento, Italy

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2007年 / 242卷 / 02期

关键词：

very weak solutions; degenerate p-harmonic equations; Orlicz-Zygmund classes;

D O I：

10.1016/j.jde.2007.07.006

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We establish regularity results for solutions of some degenerate elliptic PDEs, with right-hand side in a suitable Orlicz-Zygmund class. The nonnegative function which measures the degree of degeneracy of the ellipticity bounds is assumed to be exponentially integrable. We find that the scale of improved regularity is logarithmic and we indicate its exact dependence on the degree of the degeneracy of the problem. (c) 2007 Elsevier Inc. All rights reserved.

引用

页码：248 / 268

页数：21

共 20 条

[1]

Acerbi E, 2005, J REINE ANGEW MATH, V584, P117

[2]

ACERBI E, 1988, P S MAT INST CONT ME

[3] Gradient estimates for a class of parabolic systems [J].

Acerbi, Emilio ;

Mingione, Giuseppe .

DUKE MATHEMATICAL JOURNAL, 2007, 136 (02) :285-320

[4]

[Anonymous], 1997, DIFFER INTEGRAL EQU

[5]

BOCCARDO L, 1990, B UNIONE MAT ITAL, V4A, P219

[6]

Carozza M, 2005, ASYMPTOTIC ANAL, V44, P221

[7] COMPOSITION OF MAXIMAL OPERATORS [J].

Carozza, Menita ;

di Napoli, Antonia Passarelli .

PUBLICACIONS MATEMATIQUES, 1996, 40 (02) :397-409

[8]

Cianchi A., 1998, INT C DIFF EQ LISB 1, P306

[9] Sobolev imbedding theorems in borderline cases [J].

Fusco, N ;

Lions, PL ;

Sbordone, C .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1996, 124 (02) :561-565

[10] On the regularity of very weak minima [J].

Giachetti, D ;

Leonetti, F ;

Schianchi, R .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1996, 126 :287-296

← 1 2 →