Boundary Value Problems and Markov Processes. 1st ed. 1991

種類:

電子ブック

責任表示:

by Kazuaki Taira

出版情報:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1991

著者名:

• Taira, Kazuaki.
• SpringerLink (Online service)

シリーズ名:

Lecture Notes in Mathematics ; 1499

ISBN:

9783540466352 [3540466355]    

注記:

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.
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 introductio

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