This project will study parabolic partial differential equations in domains with rough boundaries. Using as a frame of reference recent results on the heat equation, efforts will be made to establish regularity properties of solutions to higher order parabolic equations and noncylindrical domains. Main issues to be dealt with are the spectral properties of the domains and properties of the trace semigroup. In addition to solving basic questions in differential equations, the result of this project have implications to applied areas such as probability, physics and engineering. In particular problems in colloids and furtive materials might benefit from this investment.
