When does the free boundary enter into corner points of the fixed boundary?
Shahgholian, H. (2004)
Zapiski Nauchnykh Seminarov POMI
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Displaying similar documents to “A continuity result for a quasilinear elliptic free boundary problem”
When does the free boundary enter into corner points of the fixed boundary?
Qualitative properties of the free-boundary of the Reynolds equation in lubrication.
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.
A free boundary problem for quasi-linear elliptic equations
Hans Wilhelm Alt, Luis A. Caffarelli, Avner Friedman (1984)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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On the smoothness of the free boundary in a nonlocal one-dimensional parabolic free boundary value problem
Rossitza Semerdjieva (2015)
Open Mathematics
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We consider one-dimensional parabolic free boundary value problem with a nonlocal (integro-differential) condition on the free boundary. Results on Cm-smoothness of the free boundary are obtained. In particular, a necessary and sufficient condition for infinite differentiability of the free boundary is given.
Understanding singularitiesin free boundary problems
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...
The behavior of the free boundary for the dam problem
Hans Wilhelm Alt, Gianni Gilardi (1982)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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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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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.