04246nam 22007335 450 99646648740331620200701231338.01-280-39171-597866135696393-642-12245-010.1007/978-3-642-12245-3(CKB)2550000000011510(SSID)ssj0000399635(PQKBManifestationID)11243882(PQKBTitleCode)TC0000399635(PQKBWorkID)10393512(PQKB)11356557(DE-He213)978-3-642-12245-3(MiAaPQ)EBC3065299(PPN)149062982(EXLCZ)99255000000001151020100528d2010 u| 0engurnn|008mamaatxtccrPolyharmonic Boundary Value Problems[electronic resource] Positivity Preserving and Nonlinear Higher Order Elliptic Equations in Bounded Domains /by Filippo Gazzola, Hans-Christoph Grunau, Guido Sweers1st ed. 2010.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2010.1 online resource (XVIII, 423 p. 18 illus.) Lecture Notes in Mathematics,0075-8434 ;1991Bibliographic Level Mode of Issuance: Monograph3-642-12244-2 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,0075-8434 ;1991MathematicsFunctional analysisDifferential geometryMechanicsMechanics, AppliedMathematics, generalhttps://scigraph.springernature.com/ontologies/product-market-codes/M00009Functional Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12066Differential Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M21022Solid Mechanicshttps://scigraph.springernature.com/ontologies/product-market-codes/T15010Mathematics.Functional analysis.Differential geometry.Mechanics.Mechanics, Applied.Mathematics, general.Functional Analysis.Differential Geometry.Solid Mechanics.515/.35Gazzola Filippoauthttp://id.loc.gov/vocabulary/relators/aut477156Grunau Hans-Christophauthttp://id.loc.gov/vocabulary/relators/autSweers Guidoauthttp://id.loc.gov/vocabulary/relators/autBOOK996466487403316Polyharmonic Boundary Value Problems2830981UNISA01387nam 2200361Ia 450 99639369880331620221108044727.0(CKB)3810000000005589(EEBO)2240960687(OCoLC)12200681(EXLCZ)99381000000000558919850626d1643 uy |engurbn||||a|bb|A Remonstrance to the high and mighty lords the States of Zealand[electronic resource] by the deputies of the foure classes of Zealand : concerning the welfare of the Church of England : sent over by Walter Strickland Esquire, now in Holland, imployed for the affaires of... London Printed by R. OultonMay 29, 16438 pSigned: Gulielmus Appolonij, Johannes Rogiers, Phillippus Iansborgius.Reproduction of original in Thomason Collection, British Library.eebo-0158Apollonius Willem1602 or 3-1657.1008303Lansbergen Philips van1561-1632.55115Rogiers Johan1008304Strickland Walterd. 1670.1008305EAAEAAm/cUMIWaOLNBOOK996393698803316A Remonstrance to the high and mighty lords the States of Zealand2325340UNISA