Elliptic Problems in Nonsmooth Domains

a₁ Accordingly apply Theorem B₁ belongs boundary conditions boundary value problems bounded open subset C₁ C¹¹ C² boundary Chapter coefficients Consequently convex coordinates corners Corollary corresponding cosh curvilinear polygon cut-off function defined Definition denote derivatives Dirichlet problem domains dx dy equation exists a constant exists a unique finite follows fulfils the boundary g₁ Green formula H¹(N H²(N Hölder Hölder continuous Hölder spaces holds identity implies inequality integer k₁ Lipschitz boundary Lipschitz continuous mapping neighbourhood Neumann problem norm notation obviously partition of unity plane Proof of Lemma proof of Theorem properties prove real numbers Remark result S₁ Section sequence shows singular solutions sinh smooth Sobolev spaces solution of problem subspace Ti.h u₁ V₁ vanishes vector Xn+1 zero πθ ди дт მა