A class of  non-symmetric forms on the canonical simplex of $\R^d$

Angela A. Albanese; Elisabetta M. Mangino

doi:10.3934/dcds.2009.23.639

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2009, Volume 23, Issue 3: 639-654. Doi: 10.3934/dcds.2009.23.639

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A class of non-symmetric forms on the canonical simplex of $\R^d$

Angela A. Albanese^1, and
Elisabetta M. Mangino^1,

1.
Department of Mathematics “E. De Giorgi”, University of Salento, P.O. Box 193, Via Per Arnesano, 73100 Lecce

Received: October 31, 2007

Revised: May 31, 2008

Published: August 2009

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Abstract

We introduce a class of non-symmetric bilinear forms on the d-dimen\-sional canonical simplex, related with Fleming-Viot type operators.
Strong continuity, closedness and results in the spirit of Beurling-Deny criteria are established. Moreover, under suitable assumptions, we prove that the forms satisfy the Log-Sobolev inequality. As a consequence, regularity results for semigroups generated by a class of Fleming-Viot type operators are given.

Keywords:

Semi--Dirichlet forms,
Log--Sobolev inequality,
degenerate elliptic differential operators,
simplex,
Fleming--Viot operators,
generation of $C_0$--semigroup.

Mathematics Subject Classification: Primary: 47D07, 35J70, 35B65; Secondary: 60J70.

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