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dc.contributor.advisorMaggi, Francesco, 1978-
dc.creatorMihaila, Cornelia
dc.date.accessioned2018-08-21T17:01:53Z
dc.date.available2018-08-21T17:01:53Z
dc.date.created2018-05
dc.date.issued2018-05-01
dc.date.submittedMay 2018
dc.identifierdoi:10.15781/T2R78672X
dc.identifier.urihttp://hdl.handle.net/2152/68101
dc.description.abstractIn this thesis we characterize minimizers, critical points, and almost-critical points in the capillarity droplet problem. We first develop a qualitative description of global minimizers for the classic problem describing a droplet of liquid in a container. We then prove a compactness theorem for volume-constrained almost-critical points of elliptic integrands. As applications of this theorem we obtain a description of critical points/local minimizers of elliptic energies interacting with a confinement potential and we prove an Aleksandrov-type theorem for crystalline isoperimetric problems. Lastly we develop a nonlocal analogue for the classical result of Wente, which demonstrates the axial symmetry of sessile droplets.
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.subjectCapillarity
dc.subjectCalculus of variations
dc.subjectGeometric measure theory
dc.subjectAlexandrov
dc.subjectMean curvature
dc.subjectNonlocal
dc.subjectAnisotropic
dc.subjectBubbling
dc.subjectMinimizer
dc.titleStability and behavior of critical points in the capillarity droplet problem
dc.typeThesis
dc.date.updated2018-08-21T17:01:53Z
dc.contributor.committeeMemberCaffarelli, Luis
dc.contributor.committeeMemberFigalli, Alessio
dc.contributor.committeeMemberPatrizi, Stefania
dc.contributor.committeeMemberVasseur, Alexis
dc.description.departmentMathematics
thesis.degree.departmentMathematics
thesis.degree.disciplineMathematics
thesis.degree.grantorThe University of Texas at Austin
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy
dc.creator.orcid0000-0002-4372-1225
dc.type.materialtext


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