Regularity results to the class of variational obstacle problems with variable exponent

2023/11/30 by Debraj Kar, Kar, Debraj
Biochemistry, Genetics and Molecular Biology · Mathematics · #Analysis of PDEs (math.AP) #Dermatological and Skeletal Disorders #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2311.18573

openalex publication_date 2023/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we prove local gradient estimates and higher differentiability result for the solutions of variational obstacle inequalities ∫_Ω<A(x,u,Du),D(ϕ-u)>dx≥ ∫_ΩB(x,u,Du)(ϕ-u)dx. for all ϕ∈ K_ψ(Ω). Here Ω(⊂ℝⁿ) is bounded, n≥ 2 and ψ:Ω→ℝ is called obstacle. Here we deal with variable exponent growth , namely p(.)-growth . At first we prove Calderón-Zygmund estiamte and then using this result to prove higher differentiability result in Besov scale.

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