We consider a homogeneous elliptic Dirichlet problem involving an Ornstein-Uhlenbeck operator in a half space of R^2. We show that for a particular initial datum, which is Lipschitz continuous and bounded, the second derivative of the classical solution is not uniformly continuous. In particular this implies that the well known maximal Holder-regularity results fail in general for Dirichlet problems in unbounded domains involving unbounded coefficients.

A counterexample to Schauder estimates for elliptic operators with unbounded coefficients

E. Priola
2001-01-01

Abstract

We consider a homogeneous elliptic Dirichlet problem involving an Ornstein-Uhlenbeck operator in a half space of R^2. We show that for a particular initial datum, which is Lipschitz continuous and bounded, the second derivative of the classical solution is not uniformly continuous. In particular this implies that the well known maximal Holder-regularity results fail in general for Dirichlet problems in unbounded domains involving unbounded coefficients.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11571/1251228
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 5
  • ???jsp.display-item.citation.isi??? ND
social impact