We study a class of elliptic operators $L$ that degenerate at the boundary of a bounded open set $O\subset R^d$ and possess a symmetrizing invariant measure $m$. Such operators are associated with diffusion processes in $O$ which are invariant for time reversal. After showing that the corresponding elliptic equation $\lambda u -Lu=f$ has a unique weak solution for any $\lambda > 0$ and $f\in L^2(O,m)$ we obtain new results for the characterization of the domain of $L$.

Cannarsa, P., Da Prato, G., Metafune, G., Pallara, D. (2015). Maximal regularity for gradient systems with boundary degeneracy. ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI, 26(2), 135-149 [10.4171/RLM/698].

Maximal regularity for gradient systems with boundary degeneracy

CANNARSA, PIERMARCO;
2015-01-01

Abstract

We study a class of elliptic operators $L$ that degenerate at the boundary of a bounded open set $O\subset R^d$ and possess a symmetrizing invariant measure $m$. Such operators are associated with diffusion processes in $O$ which are invariant for time reversal. After showing that the corresponding elliptic equation $\lambda u -Lu=f$ has a unique weak solution for any $\lambda > 0$ and $f\in L^2(O,m)$ we obtain new results for the characterization of the domain of $L$.
2015
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - ANALISI MATEMATICA
English
Con Impact Factor ISI
degenerate elliptic operators; diffusion processes; semigroups of operators; gradient systems; invariant measure
Cannarsa, P., Da Prato, G., Metafune, G., Pallara, D. (2015). Maximal regularity for gradient systems with boundary degeneracy. ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI, 26(2), 135-149 [10.4171/RLM/698].
Cannarsa, P; Da Prato, G; Metafune, G; Pallara, D
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/133784
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