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On the $L^p$-theory for second-order elliptic operators in divergence form with complex coefficients
2019, ter Elst, A.F.M., Haller-Dintelmann, Robert, Rehberg, Joachim, Tolksdorf, Patrick
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(Ω). 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.