Caffarelli, Luis A.2011-02-102011-02-102017-05-112011-02-102011-02-102017-05-112010-12December 2http://hdl.handle.net/2152/ETD-UT-2010-12-2562textWe 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 Hölder 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.application/pdfengNonlinear partial differential equationsFree boundary problemsLuckhaus theoremHele-shawStefan problemLipschitzAlmost minimal surfacesthesis2011-02-10