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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| Format: | Article |
| Language: | English |
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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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| _version_ | 1832558958435368960 |
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| author | Alessandro Morando Paolo Secchi |
| author_facet | Alessandro Morando Paolo Secchi |
| author_sort | Alessandro Morando |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-c687b4637ce24c89b478583f4f43c77d |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-c687b4637ce24c89b478583f4f43c77d2025-02-03T01:31:12ZengWileyInternational Journal of Differential Equations1687-96431687-96512010-01-01201010.1155/2010/524736524736Regularity of Weakly Well-Posed Characteristic Boundary Value ProblemsAlessandro Morando0Paolo Secchi1Dipartimento di Matematica, Facoltà di Ingegneria, Università di Brescia, Via Valotti, 9, 25133 Brescia, ItalyDipartimento di Matematica, Facoltà di Ingegneria, Università di Brescia, Via Valotti, 9, 25133 Brescia, ItalyWe 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.http://dx.doi.org/10.1155/2010/524736 |
| spellingShingle | Alessandro Morando Paolo Secchi Regularity of Weakly Well-Posed Characteristic Boundary Value Problems International Journal of Differential Equations |
| title | Regularity of Weakly Well-Posed Characteristic Boundary Value Problems |
| title_full | Regularity of Weakly Well-Posed Characteristic Boundary Value Problems |
| title_fullStr | Regularity of Weakly Well-Posed Characteristic Boundary Value Problems |
| title_full_unstemmed | Regularity of Weakly Well-Posed Characteristic Boundary Value Problems |
| title_short | Regularity of Weakly Well-Posed Characteristic Boundary Value Problems |
| title_sort | regularity of weakly well posed characteristic boundary value problems |
| url | http://dx.doi.org/10.1155/2010/524736 |
| work_keys_str_mv | AT alessandromorando regularityofweaklywellposedcharacteristicboundaryvalueproblems AT paolosecchi regularityofweaklywellposedcharacteristicboundaryvalueproblems |