Elliptic operators with non-local Wentzell-Robin boundary conditions

2025/02/05 by Markus Kunze, Kunze, Markus, Jonathan Mui +3
Computer Science · Mathematics · #35B09 #35P05 #47D06 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations #Primary: 35J25 #Secondary: 35B40 #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2502.03216

openalex publication_date 2025/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we study strictly elliptic, second-order differential operators on a bounded Lipschitz domain in ℝ^d, 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 characterisation 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 behaviour and, in the case of a non-positive semigroup, the weaker notion of eventual positivity of the semigroup.

Related

• Non-Positivity of the heat equation with non-local Robin boundary conditions
• Elliptic fourth-order operators with Wentzell boundary conditions on Lipschitz domains
• Semigroups Generated by Elliptic Operators in Non-Divergence Form on\n C₀(/omega)
• Quasilinear elliptic and parabolic Robin problems on Lipschitz domains
• Strict positivity for the principal eigenfunction of elliptic operators with various boundary conditions