Displaying similar documents to “A Harnack inequality approach to the regularity of free boundaries. Part III : existence theory, compactness, and dependence on X ”

A Harnack inequality approach to the regularity of free boundaries. Part I: Lipschitz free boundaries are C.

Luis A. Caffarelli (1987)

Revista Matemática Iberoamericana

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This is the first in a series of papers where we intend to show, in several steps, the existence of classical (or as classical as possible) solutions to a general two-phase free-boundary system. We plan to do so by: (a) constructing rather weak generalized solutions of the free-boundary problems, (b) showing that the free boundary of such solutions have nice measure theoretical properties (i.e., finite (n-1)-dimensional Hausdorff measure and the associated differentiability...

Free boundary regularity in Stefan type problems

Ioannis Athanasopoulos (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Regularity results of free boundaries for Stefan type problems are discussed. The influence that curvature may have on the behavior of the free boundary is studied and various open problems are also mentioned.