Maximal parabolic regularity for divergence operators including mixed boundary conditions

2009/03/02 by Robert Haller‐Dintelmann, Haller-Dintelmann, Robert, Joachim Rehberg +1 · 2 citations
Computer Science · Mathematics · #35A05 #35B65 (Primary) #35K15 #35K20 (Secondary) #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.0903.0239

openalex publication_date 2009/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that elliptic second order operators A of divergence type fulfill maximal parabolic regularity on distribution spaces, even if the underlying domain is highly non-smooth, the coefficients of A are discontinuous and A is complemented with mixed boundary conditions. Applications to quasilinear parabolic equations with non-smooth data are presented.

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• Optimal Sobolev Regularity for Second Order Divergence Elliptic Operators on Domains with Buried Boundary Parts
• Existence analysis of a three-species memristor drift-diffusion system coupled to electric networks

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