Quasilinear divergence form elliptic equations in rough domains

被引：6

作者：

Palagachev, Dian K. ^{[1
]}

机构：

[1] Politecn Bari, Dipartimento Matemat, I-70125 Bari, Italy

来源：

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS | 2010年 / 55卷 / 5-6期

关键词：

divergence form quasilinear elliptic equations; weak solvability; Holder regularity; a priori estimates; Reifenberg flat domain; BMO; COEFFICIENTS;

D O I：

10.1080/17476930903276159

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Existence and global Holder continuity are proved for the weak solution to the Dirichlet problem {div(a(ij)(x, u)D(j)u + a(t)(x, u)) = b(x, u, Du) in Omega subset of R(n), u = 0 on partial derivative Omega over Reifenberg flat domains Omega. The principal coefficients a(ij)(x, u) are discontinuous with respect to x with small BMO-norms and b(x, u, Du) grows as vertical bar Du vertical bar(r) with r < 1 + 2/n.

引用

页码：581 / 591

页数：11

共 50 条

[1] QUASILINEAR DIVERGENCE FORM PARABOLIC EQUATIONS IN REIFENBERG FLAT DOMAINS
Palagachev, Dian K.
Softova, Lubomira G.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2011, 31 (04) : 1397 - 1410
[2] Discontinuous superlinear elliptic equations of divergence form
Palagachev, Dian K.
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2009, 16 (06): : 811 - 822
[3] The Calderon-Zygmund property for quasilinear divergence form equations over Reifenberg flat domains
Palagachev, Dian K.
Softova, Lubomira G.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (05) : 1721 - 1730
[4] Discontinuous superlinear elliptic equations of divergence form
Dian K. Palagachev
Nonlinear Differential Equations and Applications NoDEA, 2009, 16
[5] Global Holder continuity of weak solutions to quasilinear divergence form elliptic equations
Palagachev, Dian K.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 359 (01) : 159 - 167
[6] NONLOCAL PROBLEMS FOR QUASILINEAR PARABOLIC EQUATIONS IN DIVERGENCE FORM
Lieberman, Gary M.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2003, : 563 - 570
[7] On the best Holder exponent for two dimensional elliptic equations in divergence form
Ricciardi, Tonia
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2008, 136 (08) : 2771 - 2783
[8] Holder regularity for non-divergence-form elliptic equations with discontinuous coefficients
Di Fazio, G.
Fanciullo, M. S.
Zamboni, P.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2013, 407 (02) : 545 - 549
[9] Recent progress in elliptic equations and systems of arbitrary order with rough coefficients in Lipschitz domains
Maz'ya, Vladimir
Shaposhnikova, Tatyana
BULLETIN OF MATHEMATICAL SCIENCES, 2011, 1 (01) : 33 - 77
[10] Quasilinear elliptic and parabolic Robin problems on Lipschitz domains
Nittka, Robin
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2013, 20 (03): : 1125 - 1155

← 1 2 3 4 5 →