Singularities in Boundary Value Problems

Accordingly addition apply assume assumptions belongs boundary value problem bounded polygonal open BRARY CALIFORNIA cj,m coefficients consequently consider continuous linear form convex coordinates corner Sj corresponding defined denote density derive differential dimensional Dirichlet boundary conditions Dirichlet problem double roots dxdt elasticity system elliptic equivalent estimate exists a constant expansion follows Fourier transform fulfilled function fv dx given Green formula Grisvard ɣjv homogeneous boundary conditions implies inequality Laplace equation Lemma LIBRARY Lipschitz open subset mixed boundary conditions Neumann Neumann problem norm notation numbers obvious operator orthogonal partial Fourier transform plane polygonal open subset polyhedral open subset Proof of Lemma proof of Theorem Proposition prove regularity result SAN DIEGO UNIVERSITY shows singular solutions Sj,m Sobolev spaces square integrable subset of R2 subspace trace UNIV variational solution vector field wave equation zero