Calculus of Variations and Geometric Measure Theory

C. Leone - G. Scilla - F. Solombrino - A. Verde

Lipschitz regularity of almost-minimizers in one-phase problems with generalized Orlicz growth

created by solombrino on 02 Aug 2025
modified by scilla on 01 Dec 2025

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Preprint

Inserted: 2 aug 2025
Last Updated: 1 dec 2025

Year: 2025

Abstract:

The optimal local Lipschitz regularity for scalar almost-minimizers of Alt-Caffarelli-type functionals \[ \mathcal{F}(v; \Omega) = \int_\Omega \varphi(x, \lvert \nabla v(x) \rvert) + \lambda \, \chi_{\{v > 0\}}(x) \, \mathrm{d}x, \] with growth function $\varphi$ a generalized Orlicz function, is established.


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