A one-dimensional free boundary problem arising in combustion theory.
Antontsev, S.N., Meirmanov, A.M., Yurinsky, V.V. (2001)
Portugaliae Mathematica. Nova Série
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Antontsev, S.N., Meirmanov, A.M., Yurinsky, V.V. (2001)
Portugaliae Mathematica. Nova Série
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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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Vilhelm Adolfsson, Luis Escauriaza, Carlos Kenig (1995)
Revista Matemática Iberoamericana
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We show that a harmonic function which vanishes continuously on an open set of the boundary of a convex domain cannot have a normal derivative which vanishes on a subset of positive surface measure. We also prove a similar result for caloric functions vanishing on the lateral boundary of a convex cylinder.
Thomas Patrick Pawlaschyk (2016)
Annales Polonici Mathematici
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We introduce the notion of the Shilov boundary for some subfamilies of upper semicontinuous functions on a compact Hausdorff space. It is by definition the smallest closed subset of the given space on which all functions of that subclass attain their maximum. For certain subfamilies with simple structure we show the existence and uniqueness of the Shilov boundary. We provide its relation to the set of peak points and establish Bishop-type theorems. As an application we obtain a generalization...
Hans Wilhelm Alt, Luis A. Caffarelli, Avner Friedman (1984)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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J. Górski (1962)
Annales Polonici Mathematici
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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.