9 citations · 52 across the 14 of their papers we have counts for
15 papers
Second order expansion for the nonlocal perimeter functional
Hans Knüpfer, Wenhui Shi
The seminal results of Bourgain, Brezis, Mironescu and Dávila show that the classical perimeter can be approximated by a family of nonlocal perimeter functionals. We consider a cor…
Higher Regularity for the Signorini Problem for the Homogeneous, Isotropic Lamé System
Angkana Rüland, Wenhui Shi
In this note we discuss the (higher) regularity properties of the Signorini problem for the homogeneous, isotropic Lamé system. Relying on an observation by Schumann \cite{Schumann…
-limit for two-dimensional charged magnetic zigzag domain walls
Hans Knüpfer, Wenhui Shi
Charged domain walls are a type of domain walls in thin ferromagnetic films which appear due to global topological constraints. The non-dimensionalized micromagnetic energy for a u…
An epiperimetric inequality approach to the parabolic Signorini problem
Wenhui Shi
In this note, we use an epiperimetric inequality approach to study the regularity of the free boundary for the parabolic Signorini problem. We show that if the "vanishing order" of…
Uniformly compressing mean curvature flow
Wenhui Shi, Dmitry Vorotnikov
Michor and Mumford showed that the mean curvature flow is a gradient flow on a Riemannian structure with a degenerate geodesic distance. It is also known to destroy the uniform den…
The gradient flow of the potential energy on the space of arcs
Wenhui Shi, Dmitry Vorotnikov
We study the gradient flow of the potential energy on the infinite-dimensional Riemannian manifold of spatial curves parametrized by the arc length, which models overdamped motion…
Optimal Regularity for the Thin Obstacle Problem with Coefficients
Angkana Rüland, Wenhui Shi
In this article we study solutions to the (interior) thin obstacle problem under low regularity assumptions on the coefficients, the obstacle and the underlying manifold. Combining…
Higher Regularity for the fractional thin obstacle problem
Herbert Koch, Angkana Rüland, Wenhui Shi
In this article we investigate the higher regularity properties of the regular free boundary in the fractional thin obstacle problem. Relying on a Hodograph-Legendre transform, we…
The Variable Coefficient Thin Obstacle Problem: Higher Regularity
Herbert Koch, Angkana Rüland, Wenhui Shi
In this article we continue our investigation of the thin obstacle problem with variable coefficients which was initiated in \cite{KRS14}, \cite{KRSI}. Using a partial Hodograph-Le…
Singular Perturbation Problem in Boundary/Fractional Combustion
Arshak Petrosyan, Wenhui Shi, Yannick Sire
Motivated by a nonlocal free boundary problem, we study uniform properties of solutions to a singular perturbation problem for a boundary-reaction-diffusion equation, where the rea…
The Variable Coefficient Thin Obstacle Problem: Optimal Regularity and Regularity of the Regular Free Boundary
Herbert Koch, Angkana Rüland, Wenhui Shi
This article deals with the variable coefficient thin obstacle problem in dimensions. We address the regular free boundary regularity, the behavior of the solution close to t…
The Variable Coefficient Thin Obstacle Problem: Carleman Inequalities
Herbert Koch, Angkana Rüland, Wenhui Shi
In this article we present a new strategy of addressing the (variable coefficient) thin obstacle problem. Our approach is based on a (variable coefficient) Carleman estimate. This…
Higher regularity of the free boundary in the elliptic Signorini problem
Herbert Koch, Arshak Petrosyan, Wenhui Shi
In this paper we study the higher regularity of the free boundary for the elliptic Signorini problem. By using a partial hodograph-Legendre transformation we show that the regular…
Parabolic Boundary Harnack Principles in Domains with Thin Lipschitz Complement
Arshak Petrosyan, Wenhui shi
We prove forward and backward parabolic boundary Harnack principles for nonnegative solutions of the heat equation in the complements of thin parabolic Lipschitz sets given as subg…
The two phase parabolic Signorini Problem
Mark Allen, Wenhui Shi
We study solutions to a variational equation that models heat control on the boundary. This problem can be thought of as the two phase parabolic Signorini problem. We show that whe…