Browsing by Subject "Lipschitz"
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Item Regularization in phase transitions with Gibbs-Thomson law(2010-12) Guillen, Nestor Daniel; Caffarelli, Luis A.; Gamba, Irene; Souganidis, Panagiotis; de La Llave, Rafael; Vasseur, Alexis; Engquist, BjornWe 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.