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Lipschitz bounds for integral functionals with (p,q)-growth conditions

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Published/Copyright: June 30, 2022

Abstract

We study local regularity properties of local minimizers of scalar integral functionals of the form

[ u ] := Ω F ( u ) - f u d x

where the convex integrand F satisfies controlled ( p , q ) -growth conditions. We establish Lipschitz continuity under sharp assumptions on the forcing term f and improved assumptions on the growth conditions on F with respect to the existing literature. Along the way, we establish an L - L 2 -estimate for solutions of linear uniformly elliptic equations in divergence form, which is optimal with respect to the ellipticity ratio of the coefficients.

MSC 2010: 49N60; 35J50

Communicated by Jan Kristensen


Award Identifier / Grant number: BE 5922/1-1

Funding statement: P. Bella was partially supported by the German Science Foundation DFG in context of the Emmy Noether Junior Research Group BE 5922/1-1.

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Received: 2022-03-01
Revised: 2022-03-22
Accepted: 2022-04-04
Published Online: 2022-06-30
Published in Print: 2024-04-01

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