Persistence of regularity of the solution to a hyperbolic boundary value problem in domain with corner

This article is about the question of persistence regularity for solution to hyperbolic boundary value problem in quarter-space. More precisely we will both consider pure and initial propose a functional space, based upon high order Sobolev space which control data leads (in same space). The proposed here contains tangential space. analysis borrows some ideas study characteristic problems half-space good derivative known be derivatives x1∂1 instead normal ∂1. For quarter-space quantity radial x1∂1+x2∂2 then recover x2∂2 using explicit formulas polar coordinates. established intrinsically by adapting method introduced author deal with without regularization methods.