Compact anisotropic stable hypersurfaces with free boundary in convex solid cones

We consider a convex solid cone C ⊂ R n + 1 with vertex at the origin and boundary ∂ C smooth away from 0. Our main result shows that a compact two-sided hypersurface Σ immersed in C with free boundary in ∂ C \ { 0 } and minimizing, up to second order, an anisotropic area functional under a volume c...

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Bibliographic Details
Published in:Calculus of variations and partial differential equations 2023-07, Vol.62 (6), Article Paper No. 185, 20
Main Author: Rosales, César
Format: Article
Language:English
Subjects:
Analysis
Calculus of Variations and Optimal Control
Optimization
Control
Free boundaries
Hyperspaces
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Systems Theory
Theoretical
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Summary:We consider a convex solid cone C ⊂ R n + 1 with vertex at the origin and boundary ∂ C smooth away from 0. Our main result shows that a compact two-sided hypersurface Σ immersed in C with free boundary in ∂ C \ { 0 } and minimizing, up to second order, an anisotropic area functional under a volume constraint is contained in a Wulff-shape. The technique of proof also works for a non-smooth convex cone C provided the boundary of Σ is away from the singular set of ∂ C .
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-023-02528-0