Show simple item record

dc.contributor.advisorFigalli, Alessioen
dc.creatorBaer, Eric Thelesen
dc.date.accessioned2012-11-20T15:58:41Zen
dc.date.available2012-11-20T15:58:41Zen
dc.date.issued2012-08en
dc.date.submittedAugust 2012en
dc.identifier.urihttp://hdl.handle.net/2152/ETD-UT-2012-08-5999en
dc.descriptiontexten
dc.description.abstractIn this thesis we collect the study of two problems in the Calculus of Variations and Partial Differential Equations. Our first group of results concern the analysis of minimizers in a variational model describing the shape of liquid drops and crystals under the influence of gravity, resting on a horizontal surface. Making use of anisotropic symmetrization techniques and an analysis of fine properties of minimizers within the class of sets of finite perimeter, we establish existence, convexity and symmetry of minimizers. In the case of smooth surface tensions, we obtain uniqueness of minimizers via an ODE characterization. In the second group of results discussed in this thesis, which is joint work with A. Vasseur, we treat a problem in compressible fluid dynamics, establishing a uniform bound from below on the temperature for a variant of the compressible Navier-Stokes-Fourier system under suitable hypotheses. This system of equations forms a mathematical model of the motion of a compressible fluid subject to heat conduction. Building upon the work of (Mellet, Vasseur 2009), we identify a class of weak solutions satisfying a localized form of the entropy inequality (adapted to measure the set where the temperature becomes small) and use a form of the De Giorgi argument for L[superscript infinity] bounds of solutions to elliptic equations with bounded measurable coefficients.en
dc.format.mimetypeapplication/pdfen
dc.language.isoengen
dc.subjectCalculus of variationsen
dc.subjectPartial differential equationsen
dc.subjectAnisotropic surface energiesen
dc.subjectSymmetrization inequalitiesen
dc.subjectCompressible fluid dynamicsen
dc.subjectTemperature boundsen
dc.titleSymmetry properties of crystals and new bounds from below on the temperature in compressible fluid dynamicsen
dc.date.updated2012-11-20T15:58:47Zen
dc.identifier.slug2152/ETD-UT-2012-08-5999en
dc.contributor.committeeMemberCaffarelli, Luisen
dc.contributor.committeeMemberGamba, Ireneen
dc.contributor.committeeMemberPavlovic, Natasaen
dc.contributor.committeeMemberMaggi, Francescoen
dc.contributor.committeeMemberVasseur, Alexisen
dc.description.departmentMathematicsen
dc.type.genrethesisen
thesis.degree.departmentMathematicsen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorUniversity of Texas at Austinen
thesis.degree.levelDoctoralen
thesis.degree.nameDoctor of Philosophyen


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record