Elst, A. F. M. ter
[VerfasserIn];
Haller-Dintelmann, Robert
[VerfasserIn];
Rehberg, Joachim
[VerfasserIn];
Tolksdorf, Patrick
[VerfasserIn]
;
Weierstraß-Institut für Angewandte Analysis und Stochastik
On the Lp-theory for second-order elliptic operators in divergence form with complex coefficients
Beschreibung:
Given a complex, elliptic coefficient function we investigate for which values of p the corresponding second-order divergence form operator, complemented with Dirichlet, Neumann or mixed boundary conditions, generates a strongly continuous semigroup on Lp(). Additional properties like analyticity of the semigroup, H-calculus and maximal regularity arealso discussed. Finally we prove a perturbation result for real coefficients that gives the whole range of p’s for small imaginary parts of the coefficients. Our results are based on the recent notion of p-ellipticity, reverse Hölder inequalities and Gaussian estimates for the real coefficients.