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REGULAR SECOND ORDER ELLIPTIC BOUNDARY VALUE PROBLEMS
SECOND ORDER ELLIPTIC BOUNDARY VALUE PROBLEMS IN CONVEX DOMAINS
Accordingly addition apply Theorem assume belongs boundary conditions boundary value problems bounded open subset Chapter constant coefficients continuous linear continuous linear form continuously differentiable convex convex function coordinates Corollary corresponding curvilinear polygon deduce defined Definition dense derivatives Dirichlet problem domains dual space dxdy elliptic boundary value equation exists a constant exists a unique follows from Theorem Fourier transform fulfills the boundary Green formula Hardy's inequality holds homogeneous hyperplane identity implies inequality integer isomorphism Laplace operator let us consider Lipschitz boundary Lipschitz continuous Lipschitz functions mapping neighborhood norm notation observe obtain obviously partition of unity polygon of class possible Proof of Lemma proof of Theorem prove real numbers resp result Section sequence shows smooth Sobolev spaces solution of problem subset of TR subspace tangential tion trace operator uniformly Lipschitz zero