Cauchy Problems in Weighted Lebesgue Spaces

Global solvability and asymptotics of semilinear parabolic Cauchy problems in ⁿ 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 ⁿ, n . In particular, the generation of analytic semigroups and the embeddings for the domains of fractional powers of elliptic operators are discussed.