Optimal regularity results in spaces of Hölder continuous functions for some infinite dimensional Ornstein–Uhlenbeck semigroup

  • Giuseppe Da Prato

    Scuola Normale Superiore, Pisa, Italy

Abstract

We consider the elliptic equation where , is -Hölder continuous and is an Ornstein−Uhlenbeck operator in a Hilbert space . We show that the mapping (with values in the space of Hilbert−Schmidt operators on ) is -Hölder continuous.

Cite this article

Giuseppe Da Prato, Optimal regularity results in spaces of Hölder continuous functions for some infinite dimensional Ornstein–Uhlenbeck semigroup. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 21 (2010), no. 1, pp. 15–31

DOI 10.4171/RLM/558