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

[21] ON THE DIRICHLET PROBLEM FOR A CLASS OF QUASILINEAR ELLIPTIC-SYSTEMS OF PARTIAL-DIFFERENTIAL EQUATIONS IN DIVERGENCE FORM
ZHANG, KW
LECTURE NOTES IN MATHEMATICS, 1988, 1306 : 262 - 277
[22] Discontinuous superlinear elliptic equations of divergence form
Palagachev, Dian K.
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2009, 16 (06): : 811 - 822
[23] Discontinuous superlinear elliptic equations of divergence form
Dian K. Palagachev
Nonlinear Differential Equations and Applications NoDEA, 2009, 16
[24] Regularity of solutions of divergence form elliptic equations
Ragusa, MA
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 128 (02) : 533 - 540
[25] Divergence form elliptic equations with discontinuous coefficients
Li, YY
Vogelius, M
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2000, 153 (02) : 91 - 151
[26] Global Estimates for Quasilinear Elliptic Equations on Reifenberg Flat Domains
Tadele Mengesha
Nguyen Cong Phuc
Archive for Rational Mechanics and Analysis, 2012, 203 : 189 - 216
[27] ON QUASILINEAR ELLIPTIC-EQUATIONS IN DOMAINS WITH CONICAL BOUNDARY POINTS
DOBROWOLSKI, M
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1989, 394 : 186 - 195
[28] Existence of solutions for quasilinear elliptic systems in divergence form with variable growth
Fu, Yongqiang
Yang, Miaomiao
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2014,
[29] QUASILINEAR ELLIPTIC SYSTEMS WITH RIGHT-HAND SIDE IN DIVERGENCE FORM
Azroul, Elhoussine
Balaadich, Farah
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2020, 50 (06) : 1935 - 1949
[30] Existence of solutions for quasilinear elliptic systems in divergence form with variable growth
Yongqiang Fu
Miaomiao Yang
Journal of Inequalities and Applications, 2014

← 1 2 3 4 5 →