On the numerical range of second order elliptic operators with mixed boundary conditions in $L^p$
Abstract
We consider second order elliptic operators with real, nonsymmetric coefficient functions which are subject to mixed boundary conditions. The aim of this paper is to provide uniform resolvent estimates for the realizations of these operators on in a most direct way and under minimal regularity assumptions on the domain. This is analogous to the main result in [Chill et al. 2006]. Ultracontractivity of the associated semigroups is also considered. All results are for two different form domains realizing mixed boundary conditions. We further consider the case of Robin -- instead of classical Neumann -- boundary conditions and also allow for operators inducing dynamic boundary conditions. The results are complemented by an intrinsic characterization of elements of the form domains inducing mixed boundary conditions.
Keywords
Cite
@article{arxiv.2005.05647,
title = {On the numerical range of second order elliptic operators with mixed boundary conditions in $L^p$},
author = {Ralph Chill and Hannes Meinlschmidt and Joachim Rehberg},
journal= {arXiv preprint arXiv:2005.05647},
year = {2020}
}