http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Semigroups, Boundary Value Problems and Markov Processes
The purpose of this book is to provide a careful and accessible account along modern lines of the subject which the title deals, as well as to discuss problems of current interest in the field. More precisely this book is devoted to the functional-analytic approach to a class of degenerate boundary value problems for second-order elliptic integro-differential operators which includes as particular cases the Dirichlet and Robin problems. This class of boundary value problems provides a new example of analytic semigroups. As an application, we construct a strong Markov process corresponding to such a diffusion phenomenon that a Markovian particle moves both by jumps and continuously in the state space until it dies at the time when it reaches the set where the particle is definitely absorbed.
Preface -- Introduction and Main Results -- Theory of Semigroups -- Markov Processes and Semigroups -- Theory of Distributions -- Theory of Pseudo-Differential Operators -- Appendix A Boundedness of Pseudo-Differential Operators -- Elliptic Boundary Value Problems -- Elliptic Boundary Value Problems and Feller Semigroups -- Appendix B Unique Solvability of Pseudo-Differential Operators -- Proof of Theorem 1 -- Proof of Theorem 2 -- A Priori Estimates -- Proof of Theorem 3 -- Proof of Theorem 4, Part (i) -- Proofs of Theorem 5 and Theorem 4, Part (ii) -- Boundary Value Problems for Waldenfels Operators -- Appendix C The Maximum Principle -- Bibliography -- Index of Symbols -- Subject Index.