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2010 Regularity of Weakly Well-Posed Characteristic Boundary Value Problems
Alessandro Morando, Paolo Secchi
Int. J. Differ. Equ. 2010: 1-39 (2010). DOI: 10.1155/2010/524736

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 L2-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.

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Alessandro Morando. Paolo Secchi. "Regularity of Weakly Well-Posed Characteristic Boundary Value Problems." Int. J. Differ. Equ. 2010 1 - 39, 2010. https://doi.org/10.1155/2010/524736

Information

Received: 9 June 2010; Accepted: 30 August 2010; Published: 2010
First available in Project Euclid: 26 January 2017

zbMATH: 1221.35431
MathSciNet: MR2746096
Digital Object Identifier: 10.1155/2010/524736

Rights: Copyright © 2010 Hindawi

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