58 citations · 105 across the 11 of their papers we have counts for
13 papers
Eigendamage: an Eigendeformation model for the variational approximation of cohesive fracture in antiplane shear deformations
Veronika Auer-Volkmann, Lisa Beck, Bernd Schmidt
We set up and investigate an approximation scheme for a variational theory of cohesive fracture in antiplane shear deformations. We consider a family of functionals acting on scala…
Optimal regularity of isoperimetric sets with Hölder densities
Lisa Beck, Eleonora Cinti, Christian Seis
We establish a regularity result for optimal sets of the isoperimetric problem with double density under mild (-)Hölder regularity assumptions on the density functions. Our main…
Exponential convergence to equilibrium for coupled systems of nonlinear degenerate drift diffusion equations
Lisa Beck, Daniel Matthes, Martina Zizza
We study the existence and long-time asymptotics of weak solutions to a system of two nonlinear drift-diffusion equations that has a gradient flow structure in the Wasserstein dist…
Eigendamage: an Eigendeformation model for the variational approximation of cohesive fracture -- a one-dimensional case study
Veronika Auer-Volkmann, Lisa Beck, Bernd Schmidt
We study an approximation scheme for a variational theory of cohesive fracture in a one-dimensional setting. Here, the energy functional is approximated by a family of functionals…
A note on the weak* and pointwise convergence of BV functions
Lisa Beck, Panu Lahti
We study pointwise convergence properties of weakly* converging sequences in . We show that, after passage to a suitable s…
Optimal Lipschitz criteria and local estimates for non-uniformly elliptic problems
Lisa Beck, Giuseppe Mingione
We report on new techniques and results in the regularity theory of general non-uniformly elliptic variational integrals. By means of a new potential theoretic approach we reproduc…
On a Neumann problem for variational functionals of linear growth
Lisa Beck, Miroslav Bulíček, Franz Gmeineder
We consider a Neumann problem for strictly convex variational functionals of linear growth. We establish the existence of minimisers among -functions provid…
Globally Lipschitz minimizers for variational problems with linear growth
Lisa Beck, Miroslav Bulíček, Erika Maringová
We study the minimization of convex, variational integrals of linear growth among all functions in the Sobolev space with prescribed boundary values (or its equivalent fo…
On the existence of integrable solutions to nonlinear elliptic systems and variational problems with linear growth
Lisa Beck, Miroslav Bulíček, Josef Málek +1
We investigate the properties of certain elliptic systems leading, a~priori, to solutions that belong to the space of Radon measures. We show that if the problem is equipped with a…
Stochastic ODEs and stochastic linear PDEs with critical drift: regularity, duality and uniqueness
Lisa Beck, Franco Flandoli, Massimiliano Gubinelli +1
In this paper linear stochastic transport and continuity equations with drift in critical spaces are considered. In this situation noise prevents shocks for the transport e…
Random perturbations of nonlinear parabolic systems
Lisa Beck, Franco Flandoli
Several aspects of regularity theory for parabolic systems are investigated under the effect of random perturbations. The deterministic theory, when strict parabolicity is assumed,…
Boundary regularity for elliptic systems under a natural growth condition
Lisa Beck
We consider weak solutions of second order nonlinear elliptic systems of the type in…
Regularity versus singularities for elliptic problems in two dimensions
Lisa Beck
In two dimensions every weak solution to a nonlinear elliptic system has Hölder continuous first derivatives provided that standard continuity, ellipticity a…