Surfaces of constant anisotropic mean curvature with free boundary in revolution surfaces

2021 ◽  
Author(s):  
Ezequiel Barbosa ◽  
Lucas Carvalho Silva
Keyword(s):  
Free Boundary ◽  
Mean Curvature ◽  
Revolution Surfaces ◽  
Anisotropic Mean Curvature

scholarly journals On a free boundary value problem for the anisotropic N-Laplace operator on an N−dimensional ring domain

2020 ◽  
Vol 28 (2) ◽  
pp. 195-208
Author(s):  
A. E. Nicolescu ◽  
S. Vlase
Keyword(s):  
Maximum Principle ◽  
Free Boundary ◽  
Boundary Value Problem ◽  
Laplace Operator ◽  
Mean Curvature ◽  
Boundary Value ◽  
Weak Sense ◽  
Ring Domain ◽  
Free Boundary Value Problem ◽  
Anisotropic Mean Curvature

AbstractIn this paper we are going to investigate a free boundary value problem for the anisotropic N-Laplace operator on a ring domain \Omega : = {\Omega _0}\backslash {\bar \Omega _1} \subset {\mathbb{R}^N}, N ≥ 2. Our aim is to show that if the problem admits a solution in a suitable weak sense, then the underlying domain Ω is a Wulff shaped ring. The proof makes use of a maximum principle for an appropriate P-function, in the sense of L.E. Payne and some geometric arguments involving the anisotropic mean curvature of the free boundary.

scholarly journals Mean curvature flow with free boundary outside a hypersphere

2017 ◽  
Vol 369 (12) ◽  
pp. 8319-8342 ◽  
Author(s):  
Glen Wheeler ◽  
Valentina-Mira Wheeler
Keyword(s):  
Free Boundary ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow

Regularity results for solutions to the c-Plateau problem with free boundary having small singular set, and generally in codimension zero

2016 ◽  
Vol 9 (3) ◽  
pp. 259-282 ◽  
Author(s):  
Leobardo Rosales
Keyword(s):  
Free Boundary ◽  
Minimization Problem ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Plateau Problem ◽  
Singular Set ◽  
Codimension Two ◽  
Rectifiable Currents ◽  
Problem With Free Boundary ◽  
Regularity Results

AbstractWe prove two results for the c-Plateau problem, introduced in [17], which is a minimization problem for integer rectifiable currents. First, we prove there is no solution to the c-Plateau problem with free boundary having singular set of finite Hausdorff codimension two measure and with regular part having constant mean curvature. Second, we prove regularity up to Hausdorff codimension seven of the free boundary of top-dimensional solutions to the c-Plateau problem.

scholarly journals The free-boundary Brakke flow

2020 ◽  
Vol 2020 (758) ◽  
pp. 95-137 ◽  
Author(s):  
Nick Edelen
Keyword(s):  
Free Boundary ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Monotonicity Formula ◽  
Local Regularity ◽  
Regularity Theorem ◽  
Elliptic Regularization ◽  
Barrier Surface ◽  
Boundary Mean Curvature

AbstractWe develop the notion of Brakke flow with free-boundary in a barrier surface. Unlike the classical free-boundary mean curvature flow, the free-boundary Brakke flow must “pop” upon tangential contact with the barrier. We prove a compactness theorem for free-boundary Brakke flows, define a Gaussian monotonicity formula valid at all points, and use this to adapt the local regularity theorem of White [23] to the free-boundary setting. Using Ilmanen’s elliptic regularization procedure [10], we prove existence of free-boundary Brakke flows.

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