Regularity of the free boundary for non degenerate phase transition problems of parabolic type
L. Fornari (2000)
Rendiconti del Seminario Matematico della Università di Padova
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L. Fornari (2000)
Rendiconti del Seminario Matematico della Università di Padova
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Hans Wilhelm Alt, Gianni Gilardi (1982)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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S. J. Alvarez (1989)
Publicacions Matemàtiques
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The hydrodynamic lubrication of a cylindrical bearing is governed by the Reynolds equation that must be satisfied by the pressure of lubricating oil. When cavitation occurrs we are carried to an elliptic free-boundary problem where the free-boundary separates the lubricated region from the cavited region. Some qualitative properties are obtained about the shape of the free-boundary as well as the localization of the cavited region.
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...
Xavier Ros-Oton, Joaquim Serra (2019)
Matematica, Cultura e Società. Rivista dell'Unione Matematica Italiana
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Free boundary problems are those described by PDEs that exhibit a priori unknown (free) interfacesor boundaries. The most classical example is the melting of ice to water (the Stefan problem). In this case, the freeboundary is the liquid-solid interface between ice and water. A central mathematical challenge in this context is to understand the regularity and singularities of free boundaries. In this paper we provide a gentle introduction to this topic by presenting some classical results...
C. Lederman (1996)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Shahgholian, H. (2004)
Zapiski Nauchnykh Seminarov POMI
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Luis A. Caffarelli (1988)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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