Gradient higher integrability for degenerate parabolic double-phase systems

2022/07/14 by Wontae Kim, Juha Kinnunen, Kim, Wontae +3 · 6 citations
Computer Science · Mathematics · #35D30 #35K55 #35K65 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2207.06807

openalex publication_date 2022/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove local higher integrability of the gradient of a weak solution to a degenerate parabolic double-phase system. This result comes with a reverse Hölder type estimate for the gradient. The proof is based on estimates in the intrinsic geometry and stopping time arguments.

Cited by

• Double phase flow under Lavrentiev phenomenon
• Gradient higher integrability of bounded solutions to parabolic double-phase systems
• Higher integrability for parabolic PDEs with generalized Orlicz growth
• Bounded solutions and interpolative gap bounds for degenerate parabolic double phase problems
• Partial regularity for parabolic systems of double phase type
• Irregular double-phase evolution problem: existence and global regularity

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• Gradient higher integrability of bounded solutions to parabolic double-phase systems
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• Very weak solutions to degenerate parabolic double-phase systems
• Bounded solutions and interpolative gap bounds for degenerate parabolic double phase problems