Topics Covered

The book treats two topics in the theory of stochastic partial differential equations: space-regularity of solutions and existence of stochastic flows.

Equations and Applications

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

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.

Reference and Results

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.

Open Problems

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.