Regularization in phase transitions with Gibbs-Thomson law

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dc.contributor.advisorCaffarelli, Luis A.en
dc.contributor.committeeMemberGamba, Ireneen
dc.contributor.committeeMemberSouganidis, Panagiotisen
dc.contributor.committeeMemberde La Llave, Rafaelen
dc.contributor.committeeMemberVasseur, Alexisen
dc.contributor.committeeMemberEngquist, Bjornen
dc.creatorGuillen, Nestor Danielen
dc.date.accessioned2011-02-10T16:48:06Zen
dc.date.available2011-02-10T16:48:06Zen
dc.date.available2011-02-10T16:48:11Zen
dc.date.issued2010-12en
dc.date.submittedDecember 2010en
dc.date.updated2011-02-10T16:48:11Zen
dc.descriptiontexten
dc.description.abstractWe study the regularity of weak solutions for the Stefan and Hele- Shaw problems with Gibbs-Thomson law under special conditions. The main result says that whenever the free boundary is Lipschitz in space and time it becomes (instantaneously) C[superscript 2,alpha] in space and its mean curvature is HoĢˆlder continuous. Additionally, a similar model related to the Signorini problem is introduced, in this case it is shown that for large times weak solutions converge to a stationary configuration.en
dc.description.departmentMathematicsen
dc.format.mimetypeapplication/pdfen
dc.identifier.urihttp://hdl.handle.net/2152/ETD-UT-2010-12-2562en
dc.language.isoengen
dc.subjectNonlinear partial differential equationsen
dc.subjectFree boundary problemsen
dc.subjectLuckhaus theoremen
dc.subjectHele-shawen
dc.subjectStefan problemen
dc.subjectLipschitzen
dc.subjectAlmost minimal surfacesen
dc.titleRegularization in phase transitions with Gibbs-Thomson lawen
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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