Improved regularity for minimizing capillary hypersurfaces
Improved regularity for minimizing capillary hypersurfaces
We give improved estimates for the size of the singular set of minimizing capillary hypersurfaces: the singular set is always of codimension at least $4$, and this estimate improves if the capillary angle is close to $0$, $\fracπ{2}$, or $π$. For capillary angles that are close to $0$ or $π$, our analysis is based on a rigorous connection between the capillary problem and the one-phase Bernoulli problem.
- Stanford University United States
- New York University United States
- University of Notre Dame United States
Mathematics - Differential Geometry, regularity, Mathematics - Analysis of PDEs, Differential Geometry (math.DG), capillary hypersurfaces, FOS: Mathematics, Fluid mechanics, one-phase Bernoulli problem, Operations research, mathematical programming, Analysis of PDEs (math.AP)
Mathematics - Differential Geometry, regularity, Mathematics - Analysis of PDEs, Differential Geometry (math.DG), capillary hypersurfaces, FOS: Mathematics, Fluid mechanics, one-phase Bernoulli problem, Operations research, mathematical programming, Analysis of PDEs (math.AP)
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