Boundary Value Problems and Markov Processes

• Main Author: Taira, Kazuaki (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.
• Series: Lecture Notes in Mathematics, 1499
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Operator theory.; Partial differential equations.; Probabilities.; Analysis.; Partial Differential Equations.; Operator Theory.; Probability Theory and Stochastic Processes.

This volume is devoted to a thorough and accessible exposition on the functional analytic approach to the problem of construction of Markov processes with Ventcel' boundary conditions in probability theory. Analytically, a Markovian particle in a domain of Euclidean space is governed by an inte...

Table of Contents:

• and Main Results
• Semigroup Theory
• L Theory of Pseudo-Differential Operators
• L Approach to Elliptic Boundary Value Problems
• Proof of Theorem 1.1
• A Priori Estimates
• Proof of Theorem 1.2
• Proof of Theorem 1.3 - Part (i)
• Proof of Theorem 1.3, Part (ii)
• Application to Semilinear Initial-Boundary Value Problems
• Concluding Remarks.