On the L^p-theory for second-order elliptic operators in divergence form with complex coefficients

2019/03/15 by ter Elst, A. F. M., Haller-Dintelmann, R., Rehberg, J. +1
#35J15 #47B44 #47D06 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1903.06692

Abstract

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 L^p(Ω). Additional properties like analyticity of the semigroup, H^∞-calculus and maximal regularity are also 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.

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