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Boundary value problems for elliptic pseudodifferential operators II

Published online by Cambridge University Press:  14 November 2011

Kazuaki Taira
Kazuaki Taira
Affiliation:
Department of Mathematics, Hiroshima University, Hagashi-Hiroshima 739, Japan
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Abstract

The purpose of this paper is to study boundary value problems for elliptic pseudodifferential operators which originate from the problem of existence of Markov processes in probability theory, generalising some results of our previous work. Our approach has a great advantage of intuitive interpretation of sufficient conditions for the unique solvability of boundary value problems in terms of Markovian motion. In fact, we prove that if a Markovian particle moves incessantly both by jumps and continuously in the state space, not being trapped in the set where no reflection phenomenon occurs, then our boundary value problem is uniquely solvable in the framework of Sobolev spaces of LP style.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 127 , Issue 2 , 1997 , pp. 395 - 405
Copyright
Copyright © Royal Society of Edinburgh 1997

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