Preprint

Inserted: 11 dec 2025
Last Updated: 11 dec 2025

Year: 2025

Abstract:

Optimal local Lipschitz regularity for scalar almost minimizers of two-phase free-boundary functionals \[ \mathcal{F}(v; \Omega) := \int_\Omega \varphi(x,\lvert\nabla v\rvert)+ \lambda_1 \chi_{\{v <0\}} + \lambda_2 \chi_{\{v > 0\}} + \min\{\lambda_1,\lambda_2\} \chi_{\{v=0\}}\, \mathrm{d}x\,, \] with growth function $\varphi$ a generalized Orlicz function and $\lambda_1,\lambda_2$ nonnegative bounded functions, is established, assuming a "small" density for either the positivity or the negativity set.

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• LeoSciSolVerTwoPhases_preprint.pdf