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 $L$.File | Dimensione | Formato | |
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