000 | 03766nam a22005535i 4500 | ||
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001 | 978-3-642-12245-3 | ||
003 | DE-He213 | ||
005 | 20190213151655.0 | ||
007 | cr nn 008mamaa | ||
008 | 100528s2010 gw | s |||| 0|eng d | ||
020 |
_a9783642122453 _9978-3-642-12245-3 |
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024 | 7 |
_a10.1007/978-3-642-12245-3 _2doi |
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_aPB _2bicssc |
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_aMAT000000 _2bisacsh |
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_aPB _2thema |
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_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. |
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300 |
_aXVIII, 423 p. 18 illus. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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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 |