Problems in non linear PDE : equilibrium configurations in periodic media and non local diffusion

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dc.contributor.advisorCaffarelli, Luis A.en
dc.contributor.committeeMemberArapostathis, Aristotleen
dc.contributor.committeeMemberde la Llave, Rafaelen
dc.contributor.committeeMemberGamba, Ireneen
dc.contributor.committeeMemberKnopf, Danen
dc.contributor.committeeMemberPavlovic, Natasaen
dc.creatorDavila, Gonzalo, 1982-en
dc.date.accessioned2012-10-25T18:01:03Zen
dc.date.available2012-10-25T18:01:03Zen
dc.date.issued2012-08en
dc.date.submittedAugust 2012en
dc.date.updated2012-10-25T18:01:09Zen
dc.descriptiontexten
dc.description.abstractWe study three different problems in non linear PDE. The first problem relates to finding equilibrium configurations in periodic media, more precisely, given an Area-Dirichlet functional J, which is periodic under integer translations and given three planes in R[superscript d], we proof there exists at least one minimizer such that it’s positive part, negative part and zero set remain at a uniform bounded distance of each plane. The second and third problem are related to non local diffusion, in the elliptic non symmetric case and parabolic case. In both cases we are interested in proving interior regularity for solutions of the aforementioned equations.en
dc.description.departmentMathematicsen
dc.format.mimetypeapplication/pdfen
dc.identifier.slug2152/ETD-UT-2012-08-6117en
dc.identifier.urihttp://hdl.handle.net/2152/ETD-UT-2012-08-6117en
dc.language.isoengen
dc.subjectNon linear equationsen
dc.subjectStable configurationsen
dc.subjectNon local diffusionen
dc.subjectNon symmetricen
dc.subjectParabolicen
dc.subjectRegularityen
dc.titleProblems in non linear PDE : equilibrium configurations in periodic media and non local diffusionen
dc.type.genrethesisen
thesis.degree.departmentMathematicsen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorUniversity of Texas at Austinen
thesis.degree.levelDoctoralen
thesis.degree.nameDoctor of Philosophyen

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