Besov regularity of inhomogeneous parabolic PDEs

Cornelia Schneider () and Flóra Orsolya Szemenyei ()
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Cornelia Schneider: Friedrich-Alexander-Universität Erlangen-Nürnberg
Flóra Orsolya Szemenyei: Friedrich-Alexander-Universität Erlangen-Nürnberg

Partial Differential Equations and Applications, 2023, vol. 4, issue 5, 1-61

Abstract: Abstract We study the regularity of solutions of parabolic partial differential equations with inhomogeneous boundary conditions on polyhedral domains $$D\subset \mathbb {R}^3$$ D ⊂ R 3 in the specific scale $$\ B^{\alpha }_{\tau ,\tau }, \ \frac{1}{\tau }=\frac{\alpha }{3}+\frac{1}{p}\ $$ B τ , τ α , 1 τ = α 3 + 1 p of Besov spaces. The regularity of the solution in this scale determines the order of approximation that can be achieved by adaptive numerical schemes. We show that for all cases under consideration the Besov regularity is high enough to justify the use of adaptive algorithms. Our results are in good agreement with the forerunner (Dahlke and Schneider in Anal Appl 17:235–291, 2019), where parabolic equations with homogeneous boundary conditions were investigated.

Keywords: Parabolic problems; Adaptive methods; Besov spaces; Weighted Sobolev spaces; Mixed weights; Domain of polyhedral type; Banach-space valued function spaces; Inhomogeneous boundary conditions; 35B65; 35K35; 35K05; 35B45; 35D30 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s42985-023-00262-y

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