To the theory of the Dirichlet and Neumann problems for strongly elliptic systems in Lipschitz domains

DOI10.1007/s10688-007-0023-xzbMath1159.35319OpenAlexW2063821173MaRDI QIDQ941865

M. S. Agranovich

Publication date: 2 September 2008

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10688-007-0023-x

zbMATH Keywords

Dirichlet problemBesov spaceNeumann problemstrong ellipticityvariational solutionLipschitz domainpotential spaceWhitney array

Mathematics Subject Classification ID

Related Items

\({H^m}\)-Conforming Virtual Elements in Arbitrary Dimension ⋮ Higher-Order Elliptic Equations in Non-Smooth Domains: a Partial Survey ⋮ Fractional powers of operators corresponding to coercive problems in Lipschitz domains ⋮ Potential type operators and transmission problems for strongly elliptic second-order systems in Lipschitz domains ⋮ The inhomogeneous Dirichlet problem for the Stokes system in Lipschitz domains with unit normal close to VMO ⋮ Spectral problems in Lipschitz domains ⋮ The Dirichlet problem for higher order equations in composition form ⋮ Layer Potentials and Boundary-Value Problems for Second Order Elliptic Operators with Data in Besov Spaces ⋮ Boundary-value problem with mixed conditions for typeless linear partial differential equations ⋮ Uniform boundary estimates in homogenization of higher-order elliptic systems ⋮ Trace and extension theorems relating Besov spaces to weighted averaged Sobolev spaces ⋮ Gradient estimates and the fundamental solution for higher-order elliptic systems with rough coefficients ⋮ Remarks on potential spaces and Besov spaces in a Lipschitz domain and on Whitney arrays on its boundary ⋮ The minimal conforming $H^k$ finite element spaces on $R^n$ rectangular grids ⋮ Dirichlet and Neumann boundary values of solutions to higher order elliptic equations ⋮ Fundamental solutions of a class of first-order linear elliptic systems ⋮ Boundary-value Problems for Higher-order Elliptic Equations in Non-smooth Domains ⋮ Recent progress in elliptic equations and systems of arbitrary order with rough coefficients in Lipschitz domains

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Regularity of variational solutions to linear boundary value problems in Lipschitz domains
• Remarks on potential spaces and Besov spaces in a Lipschitz domain and on Whitney arrays on its boundary
• The Dirichlet problem for the biharmonic equation in a Lipschitz domain
• The inhomogeneous Dirichlet problem for \(\Delta^2\) in Lipschitz domains
• Boundary layers on Sobolev-Besov spaces and Poisson's equation for the Laplacian in Lipschitz domains
• Area integral estimates for higher order elliptic equations and systems
• Regularity results for elliptic equations in Lipschitz domains
• Potential theory on Lipschitz domains in Riemannian manifolds: Sobolev-Besov space results and the Poisson problem
• Function spaces in Lipschitz domains and on Lipschitz manifolds. Characteristic functions as pointwise multipliers.
• The inhomogeneous Dirichlet problem in Lipschitz domains
• Dilation invariant estimates and the boundary Gårding inequality for higher order elliptic operators
• Necessary and sufficient conditions for the solvability of the \(L^p\) Dirichlet problem on Lipschitz domains
• The biharmonic Neumann problem in Lipschitz domains
• Remarks on strongly elliptic partial differential equations
• Boundary Integral Operators on Lipschitz Domains: Elementary Results
• On Restrictions and Extensions of the Besov and Triebel-Lizorkin Spaces with Respect to Lipschitz Domains
• Spectral problems for second-order strongly elliptic systems in smooth and non-smooth domains
• The Inhomogeneous Neumann Problem in Lipschitz Domains
• Analytic Extensions of Differentiable Functions Defined in Closed Sets
• Convex Analysis