Regularity properties for second order partial di fferential operators with unbounded coe fficients

Abstract

Linear elliptic and parabolic operators with regular and bounded coe cients have nowadays a satisfactory theory including existence, uniqueness and regularity for the solutions to the corresponding equations in several functional spaces, such as Lp spaces, H older spaces and so on. Recently, the literature shows an increasing interest towards operators with unbounded or singular coe cients. Motivations come from probability and in particular from stochastic analysis. Indeed, there is a strong connection between second order di erential operators and Markov processes.