Least supersolution approach to regularizing elliptic free boundary problems

dc.contributor.advisorCaarelli, Luisen
dc.creatorMoreira, Diego Ribeiro, 1977-en
dc.date.accessioned2008-08-28T23:43:59Zen
dc.date.available2008-08-28T23:43:59Zen
dc.date.issued2007en
dc.description.abstractIn this dissertation, we study a free boundary problem obtained as a limit as [epsilon omplies 0] to the following regularizing family of semilinear equations [Delta]u = [Beta subscript epsilon](u)F([gradient]u), where [Beta subscript epsilon] approximates the Dirac delta in the origin and F is a Lipschitz function bounded away from 0 and infinity. The least supersolution approach is used to construct solutions satisfying geometric properties of the level surfaces that are uniform. This allows to prove that the free boundary of the limit has the "right" weak geometry, in the measure theoretical sense. By the construction of some barriers with curvature, the classification of global profiles for the blow-up analysis is carried out and the limit function is proven to be a viscosity and pointwise solution (a.e) to a free boundary problem. Finally, the free boundary is proven to be a C[superscript 1, alpha] surface around H[superscript n-1] a.e. point.en
dc.description.departmentMathematicsen
dc.format.mediumelectronicen
dc.identifier.oclc175263305en
dc.identifier.urihttp://hdl.handle.net/2152/3374en
dc.language.isoengen
dc.rightsCopyright © is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works.en
dc.subject.lcshBoundary value problems--Numerical solutionsen
dc.titleLeast supersolution approach to regularizing elliptic free boundary problemsen
dc.type.genreThesisen
thesis.degree.departmentMathematicsen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorThe University of Texas at Austinen
thesis.degree.levelDoctoralen
thesis.degree.nameDoctor of Philosophyen

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