## International Journal of Differential Equations

### Regularity of Weakly Well-Posed Characteristic Boundary Value Problems

#### Abstract

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.

#### Article information

Source
Int. J. Differ. Equ., Volume 2010 (2010), Article ID 524736, 39 pages.

Dates
Accepted: 30 August 2010
First available in Project Euclid: 26 January 2017

https://projecteuclid.org/euclid.ijde/1485399927

Digital Object Identifier
doi:10.1155/2010/524736

Mathematical Reviews number (MathSciNet)
MR2746096

Zentralblatt MATH identifier
1221.35431

#### Citation

Morando, Alessandro; Secchi, Paolo. Regularity of Weakly Well-Posed Characteristic Boundary Value Problems. Int. J. Differ. Equ. 2010 (2010), Article ID 524736, 39 pages. doi:10.1155/2010/524736. https://projecteuclid.org/euclid.ijde/1485399927

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