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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2311.18573 |
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Table of Contents:
- In this paper we prove local gradient estimates and higher differentiability result for the solutions of variational obstacle inequalities \int_Ω\big<\mathcal{A}(x,u,Du),D(ϕ-u)\big>dx\geq \int_Ω\mathcal{B}(x,u,Du)(ϕ-u)dx. for all $ϕ\in \mathcal{K}_ψ(Ω)$. Here $Ω(\subset\mathbb{R}^n)$ is bounded, $n\geq 2$ and $ψ:Ω\rightarrow\mathbb{R}$ 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.