On the Continuity of Solutions to Degenerate Elliptic Equations in Two Dimensions

被引：2

作者：

Ricciardi, Tonia ^{[1
]}

Zecca, Gabriella ^{[1
]}

机构：

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

来源：

POTENTIAL ANALYSIS | 2012年 / 37卷 / 02期

关键词：

Continuity; Degenerate elliptic equations; FINITE DISTORTION; SHARP MODULUS; MAPPINGS; INEQUALITY;

D O I：

10.1007/s11118-011-9250-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study second order degenerate linear elliptic equations in divergence form in the plane. Under an exponential integrability assumption on the degenerate function we study the modulus of continuity of certain finite energy weak solutions. An application to mappings of finite distortion is also provided.

引用

页码：171 / 185

页数：15

共 22 条

[1]

[Anonymous], 2009, PRINCETON MATH SER

[2] Optimal regularity for planar mappings of finite distortion [J].

Astala, Kari ;

Gill, James T. ;

Rohde, Steffen ;

Saksman, Eero .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2010, 27 (01) :1-19

[3]

Campbell D., 2011, ANN ACAD SC IN PRESS

[4] HARNACKS INEQUALITY AND MEAN-VALUE INEQUALITIES FOR SOLUTIONS OF DEGENERATE ELLIPTIC-EQUATIONS [J].

CHANILLO, S ;

WHEEDEN, RL .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1986, 11 (10) :1111-1134

[5] On the continuity of solutions to degenerate elliptic equations [J].

Cruz-Uribe, D. ;

Di Gironimo, P. ;

Sbordone, C. .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2011, 250 (06) :2671-2686

[6]

De Giorgi E., 1957, Mem. Acad. Sci. Torino. Cl. Sci. Fis. Mat. Nat., V3, P25

[7] THE LOCAL REGULARITY OF SOLUTIONS OF DEGENERATE ELLIPTIC-EQUATIONS [J].

FABES, EB ;

KENIG, CE ;

SERAPIONI, RP .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1982, 7 (01) :77-116

[8] Irregular solutions of linear degenerate elliptic equations [J].

Franchi, B ;

Serapioni, R ;

Cassano, FS .

POTENTIAL ANALYSIS, 1998, 9 (03) :201-216

[9] A sharp weighted Wirtinger inequality and some related functional spaces [J].

Giova, Raffaella ;

Ricciardi, Tonia .

BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, 2010, 17 (02) :209-218

[10] Quasiharmonic fields [J].

Iwaniec, T ;

Sbordone, C .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2001, 18 (05) :519-572

← 1 2 3 →