Higher Integrability for Constrained Minimizers of Integral Functionals with (p,q)-Growth in low dimension

TL;DR

This paper establishes higher integrability of gradients for constrained minimizers of certain convex functionals with (p,q)-growth in low dimensions, using fractional Sobolev spaces and approximation techniques.

Contribution

It introduces a novel approach employing fractional Sobolev spaces and difference quotient estimates to prove higher summability for minimizers under (p,q)-growth conditions.

Findings

Higher gradient integrability in low dimensions

Use of fractional Sobolev spaces for regularity results

Approximation techniques based on difference quotients

Abstract

We prove higher summability for the gradient of minimizers of strongly convex integral functionals of the Calculus of Variations with (p,q)-Growth conditions in low dimension. Our procedure is set in the framework of Fractional Sobolev Spaces and renders the desired regularity as the result of an approximation technique relying on estimates obtained through a careful use of difference quotients.