Polyharmonic Boundary Value Problems : Positivity Preserving and Nonlinear Higher Order Elliptic Equations in Bounded Domains
This monograph covers higher order linear and nonlinear elliptic boundary value problems in bounded domains, mainly with the biharmonic or poly-harmonic operator as leading principal part. Underlying models and, in particular, the role of different boundary conditions are explained in detail. As for...
Kaydedildi:
| Asıl Yazarlar: | , , |
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| Materyal Türü: | Livre numérique |
| Dil: | Anglais |
| Baskı/Yayın Bilgisi: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| Edisyon: | 1st ed. 2010. |
| Seri Bilgileri: | Lecture Notes in Mathematics
1991 |
| Konular: | |
| Online Erişim: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Not: |
L'impression du document génère 438 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Polyharmonic boundary value problems, positivity preserving and nonlinear higher order elliptic equations in bounded domains, Filippo Gazzola, Hans-Christoph Grunau, Guido Sweers, Heidelberg, Springer, 2010, 1 vol. (XVIII-423 p.), Lecture notes in mathematics, 978-3-642-12244-6 • Polyharmonic boundary value problems, positivity preserving and nonlinear higher order elliptic equations in bounded domains, Filippo Gazzola, Hans-Christoph Grunau, Guido Sweers, Heidelberg, Springer, 2010, 1 vol. (XVIII-423 p.), Lecture notes in mathematics, 978-3-642-12244-6 • Polyharmonic Boundary Value Problems, Texte imprimé, 9783642122460 |
| Özet: | This monograph covers higher order linear and nonlinear elliptic boundary value problems in bounded domains, mainly with the biharmonic or poly-harmonic operator as leading principal part. Underlying models and, in particular, the role of different boundary conditions are explained in detail. As for linear problems, after a brief summary of the existence theory and Lp and Schauder estimates, the focus is on positivity or - since, in contrast to second order equations, a general form of a comparison principle does not exist - on near positivity. The required kernel estimates are also presented in detail. As for nonlinear problems, several techniques well-known from second order equations cannot be utilized and have to be replaced by new and different methods. Subcritical, critical and supercritical nonlinearities are discussed and various existence and nonexistence results are proved. The interplay with the positivity topic from the rst part is emphasized and, moreover, a far-reaching Gidas-Ni-Nirenberg-type symmetry result is included. Finally, some recent progress on the Dirichlet problem for Willmore surfaces under symmetry assumptions is discussed. |
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| Diğer Bilgileri: | L'impression du document génère 438 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Bibliyografya: | Bibliogr. Index |
| ISBN: | 9783642122453 |
| ISSN: | 1617-9692 |
| Erişim: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |