Global higher integrability for systems with p-growth structure in noncylindrical domains

2025/11/04 by Moring, Kristian, Scheven, Christoph, Schätzler, Leah
Mathematics · #Holomorphic and Operator Theory #Nonlinear Partial Differential Equations #Algebraic and Geometric Analysis

paper · doi:10.48550/arxiv.2511.02553

Abstract

We consider the Cauchy-Dirichlet problem to systems with p-growth structure with 1 < p < ∞, whose prototype is ∂_t u- div ( |Du|^p-2 Du ) = div ( |F|^p-2 F ), in a bounded noncylindrical domain E ⊂ ℝⁿ⁺¹. For p> (2(n+1))/(n+2) and domains E that satisfy suitable regularity assumptions and do not grow or shrink too fast, we prove global higher integrability of Du. The result is already new in the case p=2.

Citations

• Existence of variational solutions to doubly nonlinear systems in general noncylindrical domains
• Existence of variational solutions to doubly nonlinear systems in nondecreasing domains
• Quasilinear parabolic equations with first order terms and L¹-data in moving domains

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