This article demonstrates elliptic operators generate continuous semigroups in specific spaces, suggesting implications for spectral analysis and asymptotic behavior.
This article is concerned with strictly elliptic, second-order differential operators on a bounded Lipschitz domain in Rᵈ subject to certain non-local Wentzell–Robin boundary conditions. We prove that such operators generate strongly continuous semigroups on L²-spaces and on spaces of continuous functions. We also provide a characterization of positivity and (sub-)Markovianity of these semigroups. Moreover, based on spectral analysis of these operators, we discuss further properties of the semigroup such as asymptotic behavior and, in the case of a non-positive semigroup, the weaker notion of eventual positivity of the semigroup.
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Kunze et al. (2026) studied this question.
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