5 papers
Homogenization of Interaction Energy of Dislocation Loops
Pascal Steinke
We consider the sum of interaction energies of an array of dislocation loops placed on a homogenization lattice as the lattice spacing and diameter of the loops tend to zero. Under…
Second-Order Gamma Limit for the Cahn-Hilliard Functional with Dirichlet Boundary Conditions
Francesco Colasanto, Pascal Steinke
This paper addresses the asymptotic development of order 2 by Gamma convergence of the Cahn-Hillard functional with Dirichlet boundary conditions, where the potential has subquadra…
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…
Convergence of Allen-Cahn equations to De Giorgi's multiphase mean curvature flow
Pascal Steinke
This paper presents a conditional convergence result of solutions to the Allen--Cahn equation with arbitrary potentials to a De Giorgi type -solution to multiphase m…
Inequalities for -Functions
Pascal Steinke
In this paper, we prove trace-type Poincaré and Sobolev inequalities for the space of functions of bounded -Variation