Boundary Value Problems and Markov Processes. Lecture notes in mathematics; Bd. 1499.

Kazuaki Taira

ISBN 10: 354054996X / ISBN 13: 9783540549963

Editore: Berlin, Springer, 1991

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Ex-library with stamp and library-signature. GOOD condition, some traces of use. C-03133 354054996X Sprache: Englisch Gewicht in Gramm: 550. Codice articolo 2489032

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Titolo: Boundary Value Problems and Markov Processes...

Casa editrice: Berlin, Springer

Data di pubblicazione: 1991

Legatura: Softcover

Descrizione articolo

Riassunto:

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.

Contenuti:

1 Semigroup Theory.- 2 Lp Theory of Pseudo-Differential Operators.- 3 Lp Approach to Elliptic Boundary Value Problems.- 4 Proof of Theorem 1.- 5 A Priori Estimates.- 6 Proof of Theorem 2.- 7 Proof of Theorem 3, Part (i) .- 8 Proof of Theorem 3, Part (ii).- 9 Application to Semilinear Initial-Boundary Value Problems.