Uniqueness for volume-constraint local energy-minimizing sets in a half-space or a ball
-
Chao Xia
and
Xuwen Zhang
Abstract
In this paper, we prove a Poincaré-type inequality for any set of finite perimeter which is stable with respect to the free energy among volume-preserving perturbation, provided that the Hausdorff dimension of its singular set is at most
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11871406
Award Identifier / Grant number: 12271449
Funding statement: This work was partially supported by NSFC Nos. 11871406, 12271449.
Acknowledgements
The first author is grateful to Professor Guofang Wang for a useful discussion on this subject and his constant support. We would like to thank Professor Peter Sternberg for answering our questions regarding their paper [24]. We also would like to thank the anonymous referees for pointing out to us the boundary regularity results by De Philippis and Maggi [6, 7] for local minimizers of anisotropic free energy functionals under volume constraint and for valuable comments which helped improve the paper.
References
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Articles in the same Issue
- Frontmatter
- Another proof of the existence of homothetic solitons of the inverse mean curvature flow
- A Weierstrass extremal field theory for the fractional Laplacian
- Minimizing movements for anisotropic and inhomogeneous mean curvature flows
- A singular Yamabe problem on manifolds with solid cones
- Uniqueness for volume-constraint local energy-minimizing sets in a half-space or a ball
- Limit of solutions for semilinear Hamilton–Jacobi equations with degenerate viscosity
- Monotonicity of entire solutions to reaction-diffusion equations involving fractional p-Laplacian
- Hierarchy structures in finite index CMC surfaces
- No breathers theorem for noncompact harmonic Ricci flows with asymptotically nonnegative Ricci curvature
- Wolff potentials and local behavior of solutions to elliptic problems with Orlicz growth and measure data
- Asymptotic analysis of single-slip crystal plasticity in the limit of vanishing thickness and rigid elasticity
- On the regularity of optimal potentials in control problems governed by elliptic equations
- Sobolev embeddings and distance functions
- Effective quasistatic evolution models for perfectly plastic plates with periodic microstructure: The limiting regimes
- On the area-preserving Willmore flow of small bubbles sliding on a domain’s boundary
- Sobolev contractivity of gradient flow maximal functions
- Discrete approximation of nonlocal-gradient energies
- Symmetry and monotonicity of singular solutions to p-Laplacian systems involving a first order term
- Flat flow solution to the mean curvature flow with volume constraint
Articles in the same Issue
- Frontmatter
- Another proof of the existence of homothetic solitons of the inverse mean curvature flow
- A Weierstrass extremal field theory for the fractional Laplacian
- Minimizing movements for anisotropic and inhomogeneous mean curvature flows
- A singular Yamabe problem on manifolds with solid cones
- Uniqueness for volume-constraint local energy-minimizing sets in a half-space or a ball
- Limit of solutions for semilinear Hamilton–Jacobi equations with degenerate viscosity
- Monotonicity of entire solutions to reaction-diffusion equations involving fractional p-Laplacian
- Hierarchy structures in finite index CMC surfaces
- No breathers theorem for noncompact harmonic Ricci flows with asymptotically nonnegative Ricci curvature
- Wolff potentials and local behavior of solutions to elliptic problems with Orlicz growth and measure data
- Asymptotic analysis of single-slip crystal plasticity in the limit of vanishing thickness and rigid elasticity
- On the regularity of optimal potentials in control problems governed by elliptic equations
- Sobolev embeddings and distance functions
- Effective quasistatic evolution models for perfectly plastic plates with periodic microstructure: The limiting regimes
- On the area-preserving Willmore flow of small bubbles sliding on a domain’s boundary
- Sobolev contractivity of gradient flow maximal functions
- Discrete approximation of nonlocal-gradient energies
- Symmetry and monotonicity of singular solutions to p-Laplacian systems involving a first order term
- Flat flow solution to the mean curvature flow with volume constraint
