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Existence of solutions of quasilinear elliptic equations on manifolds with conic points

dc.contributor.advisorWitt, Ingo Prof. Dr.
dc.contributor.authorNguyen, Thi Thu Huong
dc.date.accessioned2014-05-15T09:34:53Z
dc.date.available2014-05-15T09:34:53Z
dc.date.issued2014-05-15
dc.identifier.urihttp://hdl.handle.net/11858/00-1735-0000-0022-5EB5-8
dc.identifier.urihttp://dx.doi.org/10.53846/goediss-4507
dc.language.isoengde
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/
dc.subject.ddc510de
dc.titleExistence of solutions of quasilinear elliptic equations on manifolds with conic pointsde
dc.typedoctoralThesisde
dc.contributor.refereeWitt, Ingo Prof. Dr.
dc.date.examination2013-12-13
dc.description.abstractengExistence and regularity of solutions of quasilinear elliptic equations in nonsmooth domains have been interesting topics in the development of partial differential equations. The existence of finite-energy solutions of higher-order equations, also those with degenerations and singularities, can be shown by theories of monotone operators and topological methods. There are few results about singular solutions of second-order equations involving the p-Laplacian with the Dirac distribution on the right-hand side. So far the existence of singular solutions of higher-order equations with a prescribed asymptotic behavior has not been investigated.   The aims of my dissertation are to look for finite-energy and singular solutions of quasilinear elliptic equations on manifolds with conic points. We single out realizations of the p-Laplacian in particular, (p>= 2), and a cone-degenerate operator in general, which are shown to belong to the class (S)_+. Assuming further coercivity conditions and employing mapping degree theory for generalized monotone mappings, we obtain existence for the prototypical example of the p-Laplacian and for general higher-order equations.    de
dc.contributor.coRefereeBahns, Dorothea Prof. Dr.
dc.subject.engSingular solutionsde
dc.subject.engQuasilinear elliptic equationsde
dc.subject.engManifolds with conic pointsde
dc.subject.engTopological methodsde
dc.subject.engConic p-Laplaciande
dc.identifier.urnurn:nbn:de:gbv:7-11858/00-1735-0000-0022-5EB5-8-2
dc.affiliation.instituteFakultät für Mathematik und Informatikde
dc.subject.gokfullMathematics (PPN61756535X)de
dc.identifier.ppn785833048


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