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Regularity of weakly well-posed characteristic boundary value problems. (English) Zbl 1221.35431

Summary: We study the boundary value problem for a linear first-order partial differential system with characteristic boundary of constant multiplicity. 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/conormal regularity. This is the case of problems that do not satisfy the uniform Kreiss-Lopatinskiĭ condition in the hyperbolic region of the frequency domain. Provided that the data are sufficiently smooth, we obtain the regularity of solutions, in the natural framework of weighted conormal Sobolev spaces.

MSC:

35R10 Partial functional-differential equations
35B45 A priori estimates in context of PDEs
35B65 Smoothness and regularity of solutions to PDEs
35D30 Weak solutions to PDEs
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References:

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