On Lp-Resolvent Estimates for Second-Order Elliptic Equations in Divergence Form

被引:0
作者
Byungsoo Kang
Hyunseok Kim
机构
[1] Sogang University,Department of Mathematics
来源
Potential Analysis | 2019年 / 50卷
关键词
Resolvent estimates; Elliptic equations; Dirichlet problems; Lower order terms; 35J15; 35J25; 47A10;
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学科分类号
摘要
We consider the Dirichlet problems for second-order linear elliptic equations in divergence form. The leading coefficient A has small BMO semi-norm and first-order coefficient b belongs to Lr, where n≤r<∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$n \leq r < \infty $\end{document} if n ≥ 3 and 2<r<∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$2 < r < \infty $\end{document} if n = 2. We first establish Lp-resolvent estimates on bounded domains having small Lipschitz constant when r/(r−1)<p<∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$r/(r-1) < p < \infty $\end{document}. Under the additional assumption div A ∈ Lr, we also establish Lp-resolvent estimates on bounded domains with C1,1 boundary when 1 < p < r.
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页码:107 / 133
页数:26
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