LEADER 03364nam 2200613 a 450 001 9910484111303321 005 20200520144314.0 010 $a9786613569639 010 $a9781280391712 010 $a1280391715 010 $a9783642122453 010 $a3642122450 024 7 $a10.1007/978-3-642-12245-3 035 $a(CKB)2550000000011510 035 $a(SSID)ssj0000399635 035 $a(PQKBManifestationID)11243882 035 $a(PQKBTitleCode)TC0000399635 035 $a(PQKBWorkID)10393512 035 $a(PQKB)11356557 035 $a(DE-He213)978-3-642-12245-3 035 $a(MiAaPQ)EBC3065299 035 $a(PPN)149062982 035 $a(EXLCZ)992550000000011510 100 $a20100429d2010 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aPolyharmonic boundary value problems $epositivity preserving and nonlinear higher order elliptic equations in bounded domains /$fFilippo Gazzola, Hans-Christoph Grunau, Guido Sweers 205 $a1st ed. 2010. 210 $aHeidelberg [Germany] $cSpringer$d2010 215 $a1 online resource (XVIII, 423 p. 18 illus.) 225 1 $aLecture notes in mathematics,$x0075-8434 ;$v1991 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a9783642122446 311 08$a3642122442 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 (Springer-Verlag) ;$v1991. 606 $aBoundary value problems 615 0$aBoundary value problems. 676 $a515/.35 700 $aGazzola$b Filippo$0477156 701 $aGrunau$b Hans-Christoph$0508509 701 $aSweers$b Guido$0724510 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910484111303321 996 $aPolyharmonic boundary value problems$91419819 997 $aUNINA