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Bibliographic Details
Main Author: Schäffner, Mathias
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2402.06252
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Table of Contents:
  • We study local regularity properties of local minimizer of scalar integral functionals with controlled $(p,q)$-growth in the two-dimensional plane. We establish Lipschitz continuity for local minimizer under the condition $1<p\leq q<\infty$ with $q<3p$ which improve upon the classical results valid in the regime $q<2p$. Along the way, we establish an $L^\infty$-$L^2$-estimate for solutions of linear uniformly elliptic equations in the plane which is optimal with respect to the ellipticity contrast of the coefficients.