Higher regularity for weak solutions to degenerate parabolic problems

In this paper, we study two related features of the regularity of the weak solutions to the following strongly degenerate parabolic equation u t - div D u - 1 + p - 1 Du D u = f in Ω T = Ω × ( 0 , T ) , where Ω is a bounded domain in R n for n ≥ 2 , p ≥ and T > 0 . We prove the higher differentia...

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Bibliographic Details
Published in:Calculus of variations and partial differential equations 2023-11, Vol.62 (8), Article 225
Main Authors: Gentile, Andrea, Passarelli di Napoli, Antonia
Format: Article
Language:English
Subjects:
Analysis
Calculus of Variations and Optimal Control
Optimization
Control
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Regularity
Systems Theory
Theoretical
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Summary:In this paper, we study two related features of the regularity of the weak solutions to the following strongly degenerate parabolic equation u t - div D u - 1 + p - 1 Du D u = f in Ω T = Ω × ( 0 , T ) , where Ω is a bounded domain in R n for n ≥ 2 , p ≥ and T > 0 . We prove the higher differentiability of a nonlinear function of the spatial gradient of the weak solutions, assuming only that f ∈ L loc 2 Ω T . This allows us to establish the higher integrability of the spatial gradient under the same minimal requirement on the datum f .
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-023-02564-w