Geodesic
Analytic semigroups generated on a functional extrapolation space by variational elliptic equations
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
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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. 
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     title = {Analytic semigroups generated on a functional extrapolation space by variational elliptic equations},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali},
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Vespri, Vincenzo. Analytic semigroups generated on a functional extrapolation space by variational elliptic equations. 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. http://geodesic.mathdoc.fr/item/RLINA_1988_8_82_1_a5/

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