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

Vespri, Vincenzo

Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali, Série 8, Tome 82 (1988) no. 1, pp. 29-33

Résumé

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