Abstract

In this paper we introduce and study a new class of elliptic second-order differential operators on a convex compact subset K of R^d, which are associated with a Markov operator T on C(K) and which degenerate on a suitable subset of K containing its extreme points. Among other things, we show that the closures of these operators generate Markov semigroups. Moreover, we prove that these semigroups can be approximated by means of iterates of suitable positive linear operators, which are referred to as the Bernstein-Schnabl operators associted with T. As a consequence we show that the semigroups preserve polynomials of a given degree as well as Holder continuity which gives rise some spatial regularity properties of the solutions of the relevant evolution equations.

Autore Pugliese

• Altomare Francesco , Cappelletti Montano Mirella

Tutti gli autori

• ALTOMARE F.;CAPPELLETTI MONTANO M.

Titolo volume/Rivista

Non Disponibile

Anno di pubblicazione

2014

ISSN

0022-1236

ISBN

Non Disponibile

Numero di citazioni Wos

9

Ultimo Aggiornamento Citazioni

Non Disponibile

Numero di citazioni Scopus

8

Ultimo Aggiornamento Citazioni

Non Disponibile

Settori ERC

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Codici ASJC

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