Regularity of weakly well posed non characteristic boundary value problems

摘要

We consider a boundary value problem for a system of linear partial differential equations with non regular coefficients. We assume the problem to be "weakly" well posed, in the sense that a unique L~2-solution exists, for sufficiently smooth data, and obeys an a priori energy estimate with a finite loss of tangential regularity with respect to the data. This is the case of problems that do not satisfy the uniform Kreiss-LopatinskiT condition in the hyperbolic region of the frequency domain. Provided the data are sufficiently smooth, we obtain the regularity of solutions, in the natural framework of weighted Sobolev spaces.