Polyharmonic Boundary Value Problems: Positivity Preserving and Nonlinear Higher Order Elliptic Equations in Bounded Domains - Couverture souple
Synopsis
This accessible 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. It provides rapid access to recent results and references.
Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.
Présentation de l'éditeur
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.
Présentation de l'éditeur
This accessible 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. It provides rapid access to recent results and references.
Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.
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Polyharmonic Boundary Value Problems
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Springer-Verlag Berlin and Heidelberg GmbH and Co. KG, DE, 2010
ISBN 10 : 3642122442
ISBN 13 : 9783642122446
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Paperback. Etat : New. 2010 ed. Linear elliptic equations arise in several models describing various phenomena in the applied sciences, the most famous being the second order stationary heat eq- tion or,equivalently,the membraneequation. Forthis intensivelywell-studiedlinear problem there are two main lines of results. The ?rst line consists of existence and regularity results. Usually the solution exists and "gains two orders of differen- ation" with respect to the source term. The second line contains comparison type results, namely the property that a positive source term implies that the solution is positive under suitable side constraints such as homogeneous Dirichlet bou- ary conditions. This property is often also called positivity preserving or, simply, maximum principle. These kinds of results hold for general second order elliptic problems, see the books by Gilbarg-Trudinger [198] and Protter-Weinberger [347]. For linear higher order elliptic problems the existence and regularitytype results - main, as one may say, in their full generality whereas comparison type results may fail. Here and in the sequel "higher order" means order at least four. Most interesting models, however, are nonlinear.By now, the theory of second order elliptic problems is quite well developed for semilinear, quasilinear and even for some fully nonlinear problems. If one looks closely at the tools being used in the proofs, then one ?nds that many results bene?t in some way from the positivity preserving property. Techniques based on Harnack's inequality, De Giorgi-Nash- Moser's iteration, viscosity solutions etc. N° de réf. du vendeur LU-9783642122446
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Polyharmonic Boundary Value Problems
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Springer Berlin Heidelberg Jun 2010, 2010
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ISBN 13 : 9783642122446
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Taschenbuch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 448 pp. Englisch. N° de réf. du vendeur 9783642122446
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Polyharmonic Boundary Value Problems
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Springer Berlin Heidelberg, 2010
ISBN 10 : 3642122442
ISBN 13 : 9783642122446
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Etat : New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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.This monograph covers . N° de réf. du vendeur 5049803
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Polyharmonic Boundary Value Problems: Positivity Preserving and Nonlinear Higher Order Elliptic Equations in Bounded Domains
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Polyharmonic Boundary Value Problems : Positivity Preserving and Nonlinear Higher Order Elliptic Equations in Bounded Domains
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Springer Spektrum, 2010
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Etat : Gut. Zustand: Gut | Seiten: 448 | Sprache: Englisch | Produktart: Bücher | Linear elliptic equations arise in several models describing various phenomena in the applied sciences, the most famous being the second order stationary heat eq- tion or,equivalently,the membraneequation. Forthis intensivelywell-studiedlinear problem there are two main lines of results. The ?rst line consists of existence and regularity results. Usually the solution exists and ¿gains two orders of differen- ation¿ with respect to the source term. The second line contains comparison type results, namely the property that a positive source term implies that the solution is positive under suitable side constraints such as homogeneous Dirichlet bou- ary conditions. This property is often also called positivity preserving or, simply, maximum principle. These kinds of results hold for general second order elliptic problems, see the books by Gilbarg-Trudinger [198] and Protter-Weinberger [347]. For linear higher order elliptic problems the existence and regularitytype results - main, as one may say, in their full generality whereas comparison type results may fail. Here and in the sequel ¿higher order¿ means order at least four. Most interesting models, however, are nonlinear. By now, the theory of second order elliptic problems is quite well developed for semilinear, quasilinear and even for some fully nonlinear problems. If one looks closely at the tools being used in the proofs, then one ?nds that many results bene?t in some way from the positivity preserving property. Techniques based on Harnack¿s inequality, De Giorgi-Nash- Moser¿s iteration, viscosity solutions etc. N° de réf. du vendeur 6953820/203
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Polyharmonic Boundary Value Problems
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Springer, Springer Vieweg Jun 2010, 2010
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Taschenbuch. Etat : Neu. This item is printed on demand - Print on Demand Titel. Neuware -Linear elliptic equations arise in several models describing various phenomena in the applied sciences, the most famous being the second order stationary heat eq- tion or,equivalently,the membraneequation. Forthis intensivelywell-studiedlinear problem there are two main lines of results. The rst line consists of existence and regularity results. Usually the solution exists and ¿gains two orders of differen- ation¿ with respect to the source term. The second line contains comparison type results, namely the property that a positive source term implies that the solution is positive under suitable side constraints such as homogeneous Dirichlet bou- ary conditions. This property is often also called positivity preserving or, simply, maximum principle. These kinds of results hold for general second order elliptic problems, see the books by Gilbarg-Trudinger [198] and Protter-Weinberger [347]. For linear higher order elliptic problems the existence and regularitytype results - main, as one may say, in their full generality whereas comparison type results may fail. Here and in the sequel ¿higher order¿ means order at least four. Most interesting models, however, are nonlinear. By now, the theory of second order elliptic problems is quite well developed for semilinear, quasilinear and even for some fully nonlinear problems. If one looks closely at the tools being used in the proofs, then one nds that many results bene t in some way from the positivity preserving property. Techniques based on Harnack¿s inequality, De Giorgi-Nash- Moser¿s iteration, viscosity solutions etc.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 448 pp. Englisch. N° de réf. du vendeur 9783642122446
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Polyharmonic Boundary Value Problems | Positivity Preserving and Nonlinear Higher Order Elliptic Equations in Bounded Domains
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Taschenbuch. Etat : Neu. Polyharmonic Boundary Value Problems | Positivity Preserving and Nonlinear Higher Order Elliptic Equations in Bounded Domains | Filippo Gazzola (u. a.) | Taschenbuch | Lecture Notes in Mathematics | xviii | Englisch | 2010 | Springer | EAN 9783642122446 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu. N° de réf. du vendeur 101284242
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