Cauchy problems in weighted Lebesgue spaces
Global solvability and asymptotics of semilinear parabolic Cauchy problems in are considered. Following the approach of A. Mielke [15] these problems are investigated in weighted Sobolev spaces. The paper provides also a theory of second order elliptic operators in such spaces considered over , . In particular, the generation of analytic semigroups and the embeddings for the domains of fractional powers of elliptic operators are discussed.