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010   $a1-280-39171-5
010   $a9786613569639
010   $a3-642-12245-0
024 7 $a10.1007/978-3-642-12245-3
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035   $a(DE-He213)978-3-642-12245-3
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100   $a20100528d2010      u|             0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aPolyharmonic Boundary Value Problems$b[electronic resource] $ePositivity Preserving and Nonlinear Higher Order Elliptic Equations in Bounded Domains /$fby Filippo Gazzola, Hans-Christoph Grunau, Guido Sweers
205   $a1st ed. 2010.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2010.
215   $a1 online resource (XVIII, 423 p. 18 illus.) 
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1991
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-642-12244-2 
320   $aIncludes bibliographical references and indexes.
327   $aModels 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.
330   $aThis monograph covers higher order linear and nonlinear elliptic boundary value problems in bounded domains, mainly with the biharmonic or poly-harmonic operator as leading principal part. Underlying models and, in particular, the role of different boundary conditions are explained in detail. As for linear problems, after a brief summary of the existence theory and Lp and Schauder estimates, the focus is on positivity or - since, in contrast to second order equations, a general form of a comparison principle does not exist - on ?near positivity.? The required kernel estimates are also presented in detail. As for nonlinear problems, several techniques well-known from second order equations cannot be utilized and have to be replaced by new and different methods. Subcritical, critical and supercritical nonlinearities are discussed and various existence and nonexistence results are proved. The interplay with the positivity topic from the ?rst part is emphasized and, moreover, a far-reaching Gidas-Ni-Nirenberg-type symmetry result is included. Finally, some recent progress on the Dirichlet problem for Willmore surfaces under symmetry assumptions is discussed.
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v1991
606   $aMathematics
606   $aFunctional analysis
606   $aDifferential geometry
606   $aMechanics
606   $aMechanics, Applied
606   $aMathematics, general$3https://scigraph.springernature.com/ontologies/product-market-codes/M00009
606   $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066
606   $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022
606   $aSolid Mechanics$3https://scigraph.springernature.com/ontologies/product-market-codes/T15010
615  0$aMathematics.
615  0$aFunctional analysis.
615  0$aDifferential geometry.
615  0$aMechanics.
615  0$aMechanics, Applied.
615 14$aMathematics, general.
615 24$aFunctional Analysis.
615 24$aDifferential Geometry.
615 24$aSolid Mechanics.
676   $a515/.35
700   $aGazzola$b Filippo$4aut$4http://id.loc.gov/vocabulary/relators/aut$0477156
702   $aGrunau$b Hans-Christoph$4aut$4http://id.loc.gov/vocabulary/relators/aut
702   $aSweers$b Guido$4aut$4http://id.loc.gov/vocabulary/relators/aut
906   $aBOOK
912   $a996466487403316
996   $aPolyharmonic Boundary Value Problems$92830981
997   $aUNISA