Maximal regularity for gradient systems with boundary degeneracy
Piermarco Cannarsa
Università di Roma, ItalyGiuseppe Da Prato
Scuola Normale Superiore, Pisa, ItalyGiorgio Metafune
Università del Salento, Lecce, ItalyDiego Pallara
Università degli Studi di Lecce, Italy
Abstract
We study a class of elliptic operators that degenerate at the boundary of a bounded open set and possess a symmetrizing invariant measure . Such operators are associated with diffusion processes in which are invariant for time reversal. After showing that the corresponding elliptic equation has a unique weak solution for any and , we obtain new results for the characterization of the domain of .
Cite this article
Piermarco Cannarsa, Giuseppe Da Prato, Giorgio Metafune, Diego Pallara, Maximal regularity for gradient systems with boundary degeneracy. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 26 (2015), no. 2, pp. 135–149
DOI 10.4171/RLM/698