NEUMANN AND MIXED PROBLEMS ON CURVILINEAR POLYHEDRA

We prove regularity results in L(p) Sobolev spaces. On one hand, we state some abstract results by L(p) functional techniques : exponentially decreasing estimates in dyadic partitions of cones and dihedra, operator valued symbols and Marcinkievicz's theorem. On the other hand, we derive more concrete statements with the help of estimates about the first non-zero eigenvalue of some Laplace-Beltrami operators on spherical domains.