Semigroups, Boundary Value Problems and Markov Processes

Springer Monographs in Mathematics

Kazuaki Taira

338 pages, parution le 13/11/2003

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Résumé

The purpose of this book is to provide a careful and accessible account along modern lines of the subject which the title deals, as well as to discuss problems of current interest in the field. More precisely this book is devoted to the functional-analytic approach to a class of degenerate boundary value problems for second-order elliptic integro-differential operators which includes as particular cases the Dirichlet and Robin problems. This class of boundary value problems provides a new example of analytic semigroups.
As an application, we construct a strong Markov process corresponding to such a diffusion phenomenon that a Markovian particle moves both by jumps and continuously in the state space until it dies at the time when it reaches the set where the particle is definitely absorbed.

Written for:
Researchers and graduate students

Introduction and Main Results
Theory of Semigroups
Markov Processes and Semigroups
Theory of Distributions
Theory of Pseudo-Di.erential Operators .
Elliptic Boundary Value Problems
Elliptic Boundary Value Problems and Feller Semigroups
Proof of Theorem 1.1
Proof of Theorem 1.2
A Priori Estimates
Proof of Theorem 1.3
Proof of Theorem 1.4, Part (i)
Proofs of Theorem 1.5 and Theorem 1.4, Part (ii)
Boundary Value Problems for Waldenfels Operators

A Boundedness of Pseudo-Differential Operators
B Unique Solvability of Pseudo-Differential Operators
C The Maximum Principle

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Kazuaki Taira
Parution	13/11/2003
Nb. de pages	338
Format	16 x 24
Couverture	Relié
Poids	645g
Intérieur	Noir et Blanc
EAN13	9783540406518