1st Edition

Regularity Theory and Stochastic Flows for Parabolic ISPDES

By Franco Flandoli Copyright 1995
    90 Pages
    by CRC Press

    The book treats two topics in the theory of stochastic partial differential equations: space-regularity of solutions and existence of stochastic flows. The equations considered in the book are linear parabolic with multiplicative noise, like those arising in non-linear filtering or diffusion models in randomly moving media. Regularity theory in Sobolev spaces is extensively investigated, for homogeneous and non-homogeneous boundary value problems, with a detailed analysis of the new geometrical conditions on coefficients arising as a consequence of the stochaticity. The book provides an account of regularity results that may represent a useful reference for the researcher in stochastic partial differential equations. Regularity theory is then applied to prove the existence of stochastic flows. In spite of the variety of results on stochastic flows obtained by this method, several open problems are pointed out, with the hope of stimulating further research on this subject.

    Introduction to the Series, Preface, 1 Introduction, 2 Stochastic Flows: Preliminary Comments, 3 Preliminaries on Well-Posedness and Function Spaces, 4 Regularity in Bounded Domains: Some Counterexamples, 5 Regularity Theory for Homogeneous Problems, 6 Non Homogeneous Boundary Value Problems, 7 Existence and Regularity of Stochastic Flows, 8 An Alternative Approach, Acknowledgements, References, Index


    Franco Flandoli (Universita di Pisa, Italy)