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arXiv · 2402.06252

Lipschitz bounds for nonuniformly elliptic integral functionals in the plane

Mathias Schäffner
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Abstract

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.

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Mathias Schäffner. 2024-02-09. Lipschitz bounds for nonuniformly elliptic integral functionals in the plane. https://doi.org/10.1090/proc/16878

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