Sharp regularity theory for second order hyperbolic equations of Neumann type - Part I. -L2 nonhomogeneous data

Abstract

We consider the mixed problem for a general, time independent, second order hyperbolic equation in the unknown u, with datum g ε L2(Σ) in the Neumann B.C., with datum f ε L2(Q) in the right hand side of the equation and, say, initial conditions u0=u1=0. We obtain sharp regularity results for u in Q and ù|∑ in ε, by a pseudo-differential approach on the half-space. © 1990 Fondazione Annali di Matematica Pura ed Applicata.