A strong maximum principle for minimizers of the one-phase Bernoulli problem
Nick Edelen, Luca Spolaor, Bozhidar Velichkov
TL;DR
This paper establishes a strong maximum principle for minimizers of the one-phase Bernoulli problem and constructs a related foliation, advancing understanding of the structure of these minimizers.
Contribution
It introduces a strong maximum principle for the one-phase Bernoulli functional and constructs a Hardt-Simon-type foliation for 1-homogeneous global minimizers.
Findings
Proved a strong maximum principle for the minimizers.
Constructed a Hardt-Simon-type foliation.
Enhanced understanding of the geometric structure of minimizers.
Abstract
We prove a strong maximum principle for minimizers of the one-phase Alt-Caffarelli functional. We use this to construct a Hardt-Simon-type foliation associated to any 1-homogenous global minimizer.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Advanced Mathematical Modeling in Engineering · Geometric Analysis and Curvature Flows