7 citations · 23 across the 18 of their papers we have counts for
20 papers
On the tradeoff between robustness and geometric accuracy in adversarial training
Rachel Morris, Ryan Murray, Kerrek Stinson
For non-parametric binary classification in the presence of an adversary, we prove an optimal quantitative estimate for adversarial classifiers controlling geometric accuracy, as m…
Variational properties of Perron's extremal solutions in the Bernoulli one-phase problem
Farhan Abedin, William M. Feldman, Kerrek Stinson
We study the Perron extremal solutions of the stationary one-phase Bernoulli problem. These solutions are important in several applications, but not much is known about the regular…
The -Limit Problem: Convergence of a Linear Degenerate Interface Transmission Problem
Toai Luong, Tadele Mengesha, Kerrek Stinson +2
We study the singular limit of a family of linear degenerate interface transmission problems arising from a regularization procedure in the newly proposed Two-Parameter Diffuse Dom…
Solid-solid phase transitions with space-dependent wells
Elisa Davoli, Jakob Deutsch, Manuel Friedrich +1
We investigate a second-order Modica-Mortola functional of the form \[ E_\varepsilon[u] := \int_Ω\frac{1}{\varepsilon} W(x, \nabla u) + \varepsilon|\nabla^2 u|^2 \, dx, \] which mo…
Hausdorff dimension of the singular set for Griffith almost-minimizers in the plane
Manuel Friedrich, Camille Labourie, Kerrek Stinson
We consider regularity of the crack set associated to a minimizer of the Griffith fracture energy, often used in modeling brittle materials. We show that the crack is uniformly rec…
Compactness for via concentration-compactness
William M Feldman, Kerrek Stinson
Motivated by variational models for fracture, we provide a new proof of compactness for functions without a priori bounds on the function itself. Our proof is based on the…
Convergence of a heterogeneous Allen-Cahn equation to weighted mean curvature flow
Likhit Ganedi, Alice Marveggio, Kerrek Stinson
We consider a variational model for heterogeneous phase separation, based on a diffuse interface energy with moving wells. Our main result identifies the asymptotic behavior of the…
Linearization of quasistatic fracture evolution in brittle materials
Manuel Friedrich, Pascal Steinke, Kerrek Stinson
We prove a linearization result for quasistatic fracture evolution in nonlinear elasticity. As the stiffness of the material tends to infinity, we show that rescaled displacement f…
An elliptic approximation for phase separation in a fractured material
Kerrek Stinson, Solveig Wittig
We consider a free-boundary and free-discontinuity energy connecting phase separation and fracture in an elastic material. The energy excludes the contribution of phase boundaries…
A mean curvature flow arising in adversarial training
Leon Bungert, Tim Laux, Kerrek Stinson
We connect adversarial training for binary classification to a geometric evolution equation for the decision boundary. Relying on a perspective that recasts adversarial training as…
Strong existence for free discontinuity problems in linear elasticity
Manuel Friedrich, Camille Labourie, Kerrek Stinson
In this note we show Ahlfors-regularity for a large class of quasiminimizers of the Griffith functional. This allows us to prove that, for a range of free discontinuity problems in…
An epsilon-regularity result for Griffith almost-minimizers in the plane
Manuel Friedrich, Camille Labourie, Kerrek Stinson
We present regularity results for the crack set of a minimizer for the Griffith fracture energy, arising in the variational modeling of brittle materials. In the planar setting, we…
Vector Field Models for Nematic Disclinations
Amit Acharya, Irene Fonseca, Likhit Ganedi +1
In this paper, a model for defects that was introduced in \cite{ZANV} is studied. In the literature, the setting of most models for defects is the function space SBV (special bound…
Diffuse-interface approximation and weak-strong uniqueness of anisotropic mean curvature flow
Tim Laux, Kerrek Stinson, Clemens Ullrich
The purpose of this paper is to derive anisotropic mean curvature flow as the limit of the anisotropic Allen-Cahn equation. We rely on distributional solution concepts for both the…
Gamma-convergence of a nonlocal perimeter arising in adversarial machine learning
Leon Bungert, Kerrek Stinson
In this paper we prove Gamma-convergence of a nonlocal perimeter of Minkowski type to a local anisotropic perimeter. The nonlocal model describes the regularizing effect of adversa…
Sharp Interface Limit of the Cahn-Hilliard Reaction Model for Lithium-ion Batteries
Tim Laux, Kerrek Stinson
We propose a weak solution theory for the sharp interface limit of the Cahn-Hilliard reaction model, a variational PDE for lithium-ion batteries. An essential feature of this model…
Weak solutions of Mullins-Sekerka flow as a Hilbert space gradient flow
Sebastian Hensel, Kerrek Stinson
We propose a novel weak solution theory for the Mullins-Sekerka equation primarily motivated from a gradient flow perspective. Previous existence results on weak solutions due to L…
Existence for a Cahn-Hilliard Model for Lithium-Ion Batteries with Exponential-Growth Boundary Conditions
Kerrek Stinson
The Cahn-Hilliard reaction model, a nonlinear, evolutionary PDE, was introduced to model phase separation in lithium-ion batteries. Using Butler-Volmer kinetics for electrochemical…
On Convergence of a Variational Model for Lithium-Ion Batteries
Kerrek Stinson
A singularly perturbed phase field model used to model lithium-ion batteries including chemical and elastic effects is considered. The underlying energy is given by $$I_ε[u,c ] :=…
A randomized algorithm for enumerating zonotope vertices
Kerrek Stinson, David F. Gleich, Paul G. Constantine
We propose a randomized algorithm for enumerating the vertices of a zonotope, which is a low-dimensional linear projection of a hypercube. The algorithm produces a pair of the zono…