The \(L^p\) resolvents of second-order elliptic operators of divergence form under the Dirichlet condition

DOI10.1016/j.jde.2004.05.011zbMath1274.35075OpenAlexW2005153372MaRDI QIDQ703819

Yoichi Miyazaki

Publication date: 11 January 2005

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2004.05.011

zbMATH Keywords

resolventperturbationDirichlet boundary conditionelliptic operatorreflection principle\(L^p\) theorynon-smooth coefficient

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) General theory of partial differential operators (47F05) Second-order elliptic equations (35J15) Higher-order elliptic equations (35J30)

Related Items

Higher order elliptic operators of divergence form in \(C^{1}\) or Lipschitz domains ⋮ Spectral asymptotics for Dirichlet elliptic operators with non-smooth coefficients ⋮ Schauder theory for Dirichlet elliptic operators in divergence form ⋮ On \(L^p\)-resolvent estimates for second-order elliptic equations in divergence form ⋮ The \(L^p\) theory of divergence form elliptic operators under the Dirichlet condition ⋮ \(L_p\) regularity theorem for elliptic equations in less smooth domains

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Resolvent estimates in \(W^{-1,p}\) for second order elliptic differential operators in case of mixed boundary conditions
• Equivalence between regularity theorems and heat kernel estimates for higher-order elliptic operators and systems under divergence form
• On Besov spaces and Sobolev spaces of generalized functions defined on a general region
• The \(L ^{p}\) resolvents of elliptic operators with uniformly continuous coefficients.
• Asymptotic behavior of spectral functions for elliptic operators with non-smooth coefficients
• Spectral stability under \(L^ p\)-perturbation of the second-order coefficients
• $ L_p$-estimates of the solution of the Dirichlet problem for second-order elliptic equations
• L ^p Spectral Theory of Higher-Order Elliptic Differential Operators
• Stability and Regularity of Higher Order Elliptic Operators with Measurable Coefficients

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