Maximal regularity for gradient systems with boundary degeneracy

  • Piermarco Cannarsa

    Università di Roma, Italy
  • Giuseppe Da Prato

    Scuola Normale Superiore, Pisa, Italy
  • Giorgio Metafune

    Università del Salento, Lecce, Italy
  • Diego 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