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

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<∞ if n ≥ 3 and 2<r<∞ if n = 2. We first establish Lp-resolvent estimates on bounded doma...

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Bibliographic Details
Published inPotential analysis Vol. 50; no. 1; pp. 107 - 133
Main Authors Kang, Byungsoo, Hyunseok Kim
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Nature B.V 01.01.2019
Subjects
Dirichlet problem
Divergence
Domains
Elliptic functions
Estimates
Mathematical analysis
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Summary: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<∞ if n ≥ 3 and 2<r<∞ if n = 2. We first establish Lp-resolvent estimates on bounded domains having small Lipschitz constant when r/(r−1)<p<∞. Under the additional assumption div A ∈ Lr, we also establish Lp-resolvent estimates on bounded domains with C1,1 boundary when 1 < p < r.
ISSN:0926-2601
1572-929X
DOI:10.1007/s11118-017-9675-1