Multi-Layer Potentials and Boundary Problems : for Higher-Order Elliptic Systems in Lipschitz Domains
Many phenomena in engineering and mathematical physics can be modeled by means of boundary value problems for a certain elliptic differential operator in a given domain. When the differential operator under discussion is of second order a variety of tools are available for dealing with such problems...
Enregistré dans:
| Auteurs principaux: | , |
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| Format: | Livre numérique |
| Langue: | Anglais |
| Publié: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| Édition: | 1st ed. 2013. |
| Collection: | Lecture Notes in Mathematics
2063 |
| Sujets: | |
| Accès en ligne: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Note: |
L'impression du document génère 429 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Multi-layer potentials and boundary problems, for higher-order elliptic systems in Lipschitz domains, Irina Mitrea, Marius Mitrea, 2013, Berlin [etc.], Springer, 1 vol. (X-424 p.), Lecture notes in mathematics, 978-3-642-32665-3 |
| Résumé: | Many phenomena in engineering and mathematical physics can be modeled by means of boundary value problems for a certain elliptic differential operator in a given domain. When the differential operator under discussion is of second order a variety of tools are available for dealing with such problems, including boundary integral methods, variational methods, harmonic measure techniques, and methods based on classical harmonic analysis. When the differential operator is of higher-order (as is the case, e.g., with anisotropic plate bending when one deals with a fourth order operator) only a few options could be successfully implemented. In the 1970s Alberto Calderón, one of the founders of the modern theory of Singular Integral Operators, advocated the use of layer potentials for the treatment of higher-order elliptic boundary value problems. The present monograph represents the first systematic treatment based on this approach.This research monograph lays, for the first time, the mathematical foundation aimed at solving boundary value problems for higher-order elliptic operators in non-smooth domains using the layer potential method and addresses a comprehensive range of topics, dealing with elliptic boundary value problems in non-smooth domains including layer potentials, jump relations, non-tangential maximal function estimates, multi-traces and extensions, boundary value problems with data in Whitney Lebesque spaces, Whitney Besov spaces, Whitney Sobolev- based Lebesgue spaces, Whitney Triebel Lizorkin spaces,Whitney Sobolev-based Hardy spaces, Whitney BMO and Whitney VMO spaces |
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| Description: | L'impression du document génère 429 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Bibliographie: | Bibliogr. Index |
| ISBN: | 9783642326660 |
| ISSN: | 1617-9692 |
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