Saved in:
Bibliographic Details
Main Author: Kar, Debraj
Format: Preprint
Published: 2023
Subjects:
Online Access:https://arxiv.org/abs/2311.18573
Tags: Add Tag
No Tags, Be the first to tag this record!
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.