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Analytic semigroups generated on a functional extrapolation space by variational elliptic equations

Vincenzo Vespri — 1988

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

We prove that any elliptic operator of second order in variational form is the infinitesimal generator of an analytic semigroup in the functional space C - 1 , α ⁢ ( Ω ) consinsting of all derivatives of hölder-continuous functions in Ω where Ω is a domain in ℝ n not necessarily bounded. We characterize, moreover the domain of the operator and the interpolation spaces between this and the space C - 1 , α ⁢ ( Ω ) . We prove also that the spaces C - 1 , α ⁢ ( Ω ) can be considered as extrapolation spaces relative to suitable non-variational operators....

Analytic semigroups generated on a functional extrapolation space by variational elliptic equations

Vincenzo Vespri — 1988

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

We prove that any elliptic operator of second order in variational form is the infinitesimal generator of an analytic semigroup in the functional space C - 1 , α ⁢ ( Ω ) consinsting of all derivatives of hölder-continuous functions in Ω where Ω is a domain in ℝ n not necessarily bounded. We characterize, moreover the domain of the operator and the interpolation spaces between this and the space C - 1 , α ⁢ ( Ω ) . We prove also that the spaces C - 1 , α ⁢ ( Ω ) can be considered as extrapolation spaces relative to suitable non-variational operators....

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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