The biharmonic Neumann problem in Lipschitz domains
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Publication:2495346
DOI10.1007/BF02393222zbMath1216.35021MaRDI QIDQ2495346
Publication date: 6 July 2006
Published in: Acta Mathematica (Search for Journal in Brave)
Boundary value problems for higher-order elliptic equations (35J40) PDEs in connection with mechanics of deformable solids (35Q74)
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Cites Work
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- On the theory of harmonic functions of several variables
- Layer potentials and boundary value problems for elliptic systems in Lipschitz domains
- Boundary value problems for the systems of elastostatics in Lipschitz domains
- Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains
- The Dirichlet problem for the biharmonic equation in a Lipschitz domain
- Hardy spaces and the Neumann problem in \(L^ p\) for Laplace's equation in Lipschitz domains
- A course in elasticity. Translated by F. A. Ficken, with the editorial assistance of D. A. Simons
- L'intégrale de Cauchy définit un opératuer borne sur \(L^ 2 \)pour les courbes lipschitziennes
- Potential techniques for boundary value problems on \(C^1\)-domains
- A maximum principle for biharmonic functions in Lipschitz and \(C^ 1\) domains
- Area integral estimates for higher order elliptic equations and systems
- The method of layer potentials in electromagnetic scattering theory on nonsmooth domains
- The Dirichlet problem for the Stokes system on Lipschitz domains
- Dilation invariant estimates and the boundary Gårding inequality for higher order elliptic operators
- On the Poisson integral for Lipschitz and $C^{1}$-domains
- The Neumann problem on Lipschitz domains
- Area Integral Estimates for the Biharmonic Operator in Lipschitz Domains
- The Dirichlet Problem in L p for the Biharmonic Equation on Lipschitz Domains
- Abstract green formula and applications to boundary integral equations
- A new system of boundary integral equations for plates with free edges
- On the eigenvalues and eigenfunctions of elastic plates
- Potential theory