03364nam 2200613 a 450 991048411130332120200520144314.09786613569639978128039171212803917159783642122453364212245010.1007/978-3-642-12245-3(CKB)2550000000011510(SSID)ssj0000399635(PQKBManifestationID)11243882(PQKBTitleCode)TC0000399635(PQKBWorkID)10393512(PQKB)11356557(DE-He213)978-3-642-12245-3(MiAaPQ)EBC3065299(PPN)149062982(EXLCZ)99255000000001151020100429d2010 uy 0engurnn|008mamaatxtccrPolyharmonic boundary value problems positivity preserving and nonlinear higher order elliptic equations in bounded domains /Filippo Gazzola, Hans-Christoph Grunau, Guido Sweers1st ed. 2010.Heidelberg [Germany] Springer20101 online resource (XVIII, 423 p. 18 illus.) Lecture notes in mathematics,0075-8434 ;1991Bibliographic Level Mode of Issuance: Monograph9783642122446 3642122442 Includes bibliographical references and indexes.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 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.Lecture notes in mathematics (Springer-Verlag) ;1991.Boundary value problemsBoundary value problems.515/.35Gazzola Filippo477156Grunau Hans-Christoph508509Sweers Guido724510MiAaPQMiAaPQMiAaPQBOOK9910484111303321Polyharmonic boundary value problems1419819UNINA