Fractional Derivatives and Fractional Powers as Tools in Understanding Wentzell Boundary Value Problems for Pseudo-Differential Operators Generating Markov Processes

Abstract

Wentzell boundary value problem for pseudo-differential operators generating Markov processes but not satisfying the transmission condition are not well understood. Studying fractional derivatives and fractional powers of such operators gives some insights in this problem. Since an L^p – theory for such operators will provide a helpful tool we investigate the L^p –domains of certain model operators.