DIRICHLET PROBLEMS FOR SECOND ORDER LINEAR ELLIPTIC EQUATIONS WITH L1-DATA

被引：2

作者：

Kim, H. ^{[1
]}

Oh, J. I. S. U. ^{[2
]}

机构：

[1] Sogang Univ, Dept Math, Seoul, South Korea

[2] North Carolina State Univ, Dept Stat, Raleigh, NC USA

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2023年 / 22卷 / 06期

基金：

新加坡国家研究基金会;

关键词：

Dirichlet problems; elliptic equations; drifts; existence; uniqueness; DIVERGENCE FORM; INTERPOLATION; OPERATORS;

D O I：

10.3934/cpaa.2023051

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

-div (ADu) + div (ub) + cu = div F in S2 and u = 0 on partial differential S2, where A = [aij] is bounded, uniformly elliptic, and of vanishing mean oscillation (VMO). The main purpose of this paper is to study unique solvability for both problems with L1-data. We prove that if S2 is of class C1, div A + b E Ln,1(S2; Rn), c E Ln2,1(S2) n Ls(S2) for some 1 < s < 32 , and c > 0 in S2, then for each f E L1(S2), there exists a unique weak solution in 1, n n-1 ,infinity W (S2) of the first problem. Moreover, under the additional condition that S2 is of class C1,1 and c E Ln,1(S2), we show that for each FE L1(S2; Rn),

引用

页码：1899 / 1917

页数：19

共 25 条

[1] REAL INTERPOLATION OF SOBOLEV SPACES ON SUB-DOMAINS OF RN [J].