On the numerical range of second order elliptic operators with mixed\n boundary conditions in L^p

2020/05/12 by Ralph Chill, Chill, Ralph, Hannes Meinlschmidt +3 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Equations and Boundary Problems #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2005.05647

Abstract

We consider second order elliptic operators with real, nonsymmetric\ncoefficient functions which are subject to mixed boundary conditions. The aim\nof this paper is to provide uniform resolvent estimates for the realizations of\nthese operators on L^p in a most direct way and under minimal regularity\nassumptions on the domain. This is analogous to the main result in [Chill et\nal. 2006]. Ultracontractivity of the associated semigroups is also considered.\nAll results are for two different form domains realizing mixed boundary\nconditions. We further consider the case of Robin -- instead of classical\nNeumann -- boundary conditions and also allow for operators inducing dynamic\nboundary conditions. The results are complemented by an intrinsic\ncharacterization of elements of the form domains inducing mixed boundary\nconditions.\n

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