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Continuity for bounded solutions of multiphase Stefan problem

Emmanuele DiBenedetto, Vincenzo Vespri (1994)

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

We establish the continuity of bounded local solutions of the equation β u t = Δ u . Here β is any coercive maximal monotone graph in R × R , bounded for bounded values of its argument. The multiphase Stefan problem and the Buckley-Leverett model of two immiscible fluids in a porous medium give rise to such singular equations.

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