Regularity of Weakly Well-Posed Characteristic Boundary Value Problems
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 e...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2010-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2010/524736 |
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| 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 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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| ISSN: | 1687-9643 1687-9651 |