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Field name	Details
Dewey Class	515
Title	Boundary Value Problems and Markov Processes ([EBook] /) / by Kazuaki Taira.
Author	Taira, Kazuaki
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : : Springer Berlin Heidelberg : : Imprint: Springer, , 1991.
Physical Details	IX, 132 p. : online resource.
Series	Lecture Notes in Mathematics 0075-8434 ; ; 1499
ISBN	9783540466352
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/BFb0092029
Links to Related Works	Subject References: Analysis . Analysis (Mathematics) . Mathematical analysis . Mathematics . Probabilities . Probability theory and stochastic processes . Authors: Taira, Kazuaki . Corporate Authors: SpringerLink (Online service) . Series: Lecture Notes in Mathematics . Classification: 515 .

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Boundary Value Problems and Markov Processes

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