## International Journal of Differential Equations

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

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

Alessandro Morando and Paolo Secchi

#### 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**

Received: 9 June 2010

Accepted: 30 August 2010

First available in Project Euclid: 26 January 2017

**Permanent link to this document**

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