International Journal of Differential Equations
Volume 2010 (2010), Article ID 524736, 39 pages
Research Article

Regularity of Weakly Well-Posed Characteristic Boundary Value Problems

Dipartimento di Matematica, Facoltà di Ingegneria, Università di Brescia, Via Valotti, 9, 25133 Brescia, Italy

Received 9 June 2010; Accepted 30 August 2010

Academic Editor: Alberto Cabada

Copyright © 2010 Alessandro Morando and Paolo Secchi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.