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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Published in | Potential analysis Vol. 50; no. 1; pp. 107 - 133 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Dordrecht
Springer Nature B.V
01.01.2019
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Subjects | |
Online Access | Get full text |
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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. |
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ISSN: | 0926-2601 1572-929X |
DOI: | 10.1007/s11118-017-9675-1 |