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math.AP2023
Lipschitz regularity of almost minimizers in a Bernoulli problem with non-standard growth
João Vitor da Silva, Analía Silva, Hernán Vivas
In this work we establish the optimal Lipschitz regularity for non-negative almost minimizers of the one-phase Bernoulli-type functional $$ \mathcal{J}_{\mathrm{G}}(u,Ω) := \int_Ω\…
math.DG2023
A PDE approach to the existence and regularity of surfaces of minimum mean curvature variation
L. A. Caffarelli, P. R. Stinga, H. Vivas
We develop an analytic theory of existence and regularity of surfaces (given by graphs) arising from the geometric minimization problem $$\min_{\mathcal{M}}\frac{1}{2}\int_{\mathca…