JournalsrlmVol. 21, No. 1pp. 15–31

Optimal regularity results in spaces of Hölder continuous functions for some infinite dimensional Ornstein&#8722Uhlenbeck semigroup

  • Giuseppe Da Prato

    Scuola Normale Superiore, Pisa, Italy
Optimal regularity results in spaces of Hölder continuous functions for some infinite dimensional Ornstein&#8722Uhlenbeck semigroup cover

Abstract

We consider the elliptic equation λ φ – Lφ = f where λ > 0, f is θ-Hölder continuous and L is an Ornstein−Uhlenbeck operator in a Hilbert space H. We show that the mapping D_2_φ (with values in the space of Hilbert−Schmidt operators on H) is θ-Hölder continuous.

Cite this article

Giuseppe Da Prato, Optimal regularity results in spaces of Hölder continuous functions for some infinite dimensional Ornstein&#8722Uhlenbeck semigroup. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 21 (2010), no. 1, pp. 15–31

DOI 10.4171/RLM/558