Preprint series: 04-20, Reports on Analysis

MSC:

35J70 Elliptic partial differential equations of degenerate type

35K65 Parabolic partial differential equations of degenerate type

47D06 One-parameter semigroups and linear evolution equations

Abstract: We study the generation of an analytic semigroup in $L^p(\R^d)$ and the
determination of the domain for a class of second order elliptic operators
with unbounded coefficients in $\R^d$. We also establish the maximal
regularity of type $L^q$--$L^p$ for the corresponding inhomogeneous parabolic
equation. In contrast to the previous literature the coefficients of the
second derivatives are not required to be strictly elliptic or bounded.
Interior singularities of the lower order terms are also discussed.

Keywords: Unbounded and degenerate coefficients, analytic semigroups, maximal regularity

Upload: 2004-05-26

Update: 2004 -05 -26