Research Catalog

Title

Boundary value problems and Markov processes / Kazuaki Taira.

Author

Taira, Kazuaki

Publication

Berlin ; New York : Springer-Verlag, ©1991.

Items in the Library & Off-site

Details

Description

132 pages : illustrations; 25 cm.

Summary

Focussing on the interrelations of the subjects of Markov processes, analytic semigroups and elliptic boundary value problems, this monograph provides a careful and accessible exposition of functional methods in stochastic analysis. The author studies a class of boundary value problems for second-order elliptic differential operators which includes as particular cases the Dirichlet and Neumann problems, and proves that this class of boundary value problems provides a new example of analytic semigroups both in the Lp topology and in the topology of uniform convergence. As an application, one can construct analytic semigroups corresponding to the diffusion phenomenon of a Markovian particle moving continuously in the state space until it "dies", at which time it reaches the set where the absorption phenomenon occurs. A class of initial-boundary value problems for semilinear parabolic differential equations is also considered. This monograph will appeal to both advanced students and researchers as an introduction to the three interrelated subjects in analysis, providing powerful methods for continuing research.

Series Statement

Lecture notes in mathematics ; 1499

Uniform Title

Lecture notes in mathematics (Springer-Verlag) ; 1499.

Subject

• Boundary value problems
• Differential equations, Elliptic
• Markov processes
• Semigroups
• Markov Chains
• Semigroups
• Boundary value problems
• Differential equations, Elliptic
• Markov processes
• Elliptischer Differentialoperator
• Elliptisches Randwertproblem
• Feller-Halbgruppe
• Markov-Prozess
• Randwertproblem

Bibliography (note)

• Includes bibliographical references (p. [114]-115) and index.

Additional Formats (note)

• Also available in an electronic version.

Contents

And results -- Semigroup theory -- L p theory of pseudo-differential operators -- L p approach to elliptic boundary value problems -- Proof of Theorem 1 -- A priori estimates -- Proof of Theorem 2 -- Proof of Theorem 3 -- Part (i) -- Proof of Theorem 3 -- Part (ii) -- Application to semilinear initial-boundary value problems.

ISBN

• 354054996X
• 9783540549963
• 038754996X
• 9780387549965

LCCN

92148286

OCLC

• ocm25506795
• 25506795
• SCSB-1974322

Owning Institutions

Princeton University Library