# Sharp regularity theory for second order hyperbolic equations of Neumann type

Part I. —

*L*_{2}nonhomogeneous dataArticle

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## Summary

We consider the mixed problem for a general, time independent, second order hyperbolic equation in the unknown u, with datum g ε L_{2}(Σ) in the Neumann B.C., with datum f ε L_{2}(Q) in the right hand side of the equation and, say, initial conditions u_{0}=u_{1}=0. We obtain sharp regularity results for u in Q and ù|_{∑} in ε, by a pseudo-differential approach on the half-space.

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