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Regular secondorder elliptic boundary value problems
Secondorder elliptic boundary value problems in convex
Secondorder elliptic boundary value problems in polygons
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Accordingly apply Theorem Assume in addition boundary conditions boundary value problems bounded open subset bounded support C2 boundary Chapter continuous linear continuous linear form continuously differentiable convex coordinates corners Corollary corresponding cosh curvilinear polygon cut-off function defined Definition derivatives differential operators Dirichlet problem domains dx dy equation exists a constant exists a unique Fourier transform fulfil the assumptions fulfils the boundary Green formula Hardy's inequality holds homogeneous identity implies integer Laplace operator let us consider Lipschitz boundary Lipschitz continuous mapping neighbourhood Neumann boundary condition Neumann problem norm notation obtain obviously particular partition of unity plane polygon of class Proof of Lemma proof of Theorem prove real numbers Remark result Section sequence shows singular solutions sinh smooth Sobolev spaces solution of problem subset of U2 subspace take the limit tangential trace theorem vanishes vector zero