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020 _a9783642122453
_9978-3-642-12245-3
024 7 _a10.1007/978-3-642-12245-3
_2doi
050 4 _aQA1-939
072 7 _aPB
_2bicssc
072 7 _aMAT000000
_2bisacsh
072 7 _aPB
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082 0 4 _a510
_223
100 1 _aGazzola, Filippo.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aPolyharmonic Boundary Value Problems
_h[electronic resource] :
_bPositivity Preserving and Nonlinear Higher Order Elliptic Equations in Bounded Domains /
_cby Filippo Gazzola, Hans-Christoph Grunau, Guido Sweers.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2010.
300 _aXVIII, 423 p. 18 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1991
505 0 _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.
520 _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 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.
650 0 _aMathematics.
650 0 _aFunctional analysis.
650 0 _aGlobal differential geometry.
650 0 _aMechanics.
650 0 _aMechanics, Applied.
650 1 4 _aMathematics, general.
_0http://scigraph.springernature.com/things/product-market-codes/M00009
650 2 4 _aFunctional Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12066
650 2 4 _aDifferential Geometry.
_0http://scigraph.springernature.com/things/product-market-codes/M21022
650 2 4 _aSolid Mechanics.
_0http://scigraph.springernature.com/things/product-market-codes/T15010
700 1 _aGrunau, Hans-Christoph.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aSweers, Guido.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642122446
776 0 8 _iPrinted edition:
_z9783642122460
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1991
856 4 0 _uhttps://doi.org/10.1007/978-3-642-12245-3
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c11494
_d11494