Polyharmonic Boundary Value Problems [[electronic resource] ] : Positivity Preserving and Nonlinear Higher Order Elliptic Equations in Bounded Domains / / by Filippo Gazzola, Hans-Christoph Grunau, Guido Sweers
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| Autore: |
Gazzola Filippo
|
| Titolo: |
Polyharmonic Boundary Value Problems [[electronic resource] ] : Positivity Preserving and Nonlinear Higher Order Elliptic Equations in Bounded Domains / / by Filippo Gazzola, Hans-Christoph Grunau, Guido Sweers
|
| Pubblicazione: | Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2010 |
| Edizione: | 1st ed. 2010. |
| Descrizione fisica: | 1 online resource (XVIII, 423 p. 18 illus.) |
| Disciplina: | 515/.35 |
| Soggetto topico: | Mathematics |
| Functional analysis | |
| Differential geometry | |
| Mechanics | |
| Mechanics, Applied | |
| Mathematics, general | |
| Functional Analysis | |
| Differential Geometry | |
| Solid Mechanics | |
| Persona (resp. second.): | GrunauHans-Christoph |
| SweersGuido | |
| Note generali: | Bibliographic Level Mode of Issuance: Monograph |
| Nota di bibliografia: | Includes bibliographical references and indexes. |
| Nota di contenuto: | Models of Higher Order -- Linear Problems -- Eigenvalue Problems -- Kernel Estimates -- Positivity and Lower Order Perturbations -- Dominance of Positivity in Linear Equations -- Semilinear Problems -- Willmore Surfaces of Revolution. |
| Sommario/riassunto: | 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 first 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. |
| Titolo autorizzato: | Polyharmonic Boundary Value Problems |
| ISBN: | 1-280-39171-5 |
| 9786613569639 | |
| 3-642-12245-0 | |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 996466487403316 |
| Lo trovi qui: | Univ. di Salerno |
| Opac: | Controlla la disponibilità qui |
Serie:
Lecture Notes in Mathematics, . 0075-8434 ; ; 1991