Helmholtz-Institute Ulm

output

20072026

most citedFAIR data enabling new horizons for materials research

252 citations

researchers with a paper here

Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

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16 papers · 1 filter

math.AP2024★ 1 cited

Dynamics of Elastic Wires: Preserving Area without Nonlocality

Leonie Langer

We derive an $H^{- 1}$ -gradient flow of the elastic energy which preserves the enclosed area of evolving planar curves. For this new sixth-order evolution equation, we prove a globa…

math.AP2023★ 1 cited

Singularities of the hyperbolic elastic flow: Convergence, quantization and blow-ups

Manuel Schlierf

We study the elastic flow of closed curves and of open curves with clamped boundary conditions in the hyperbolic plane. While global existence and convergence toward critical point…

math.AP2023

Nittka's invariance criterion and Hilbert space valued parabolic equations in $L_{p}$

W. Arendt, A. F. M. ter Elst, M. Sauter

Nittka gave an efficient criterion on a form defined on $L_{2} (Ω)$ which implies that the associated semigroup is $L_{p}$ -invariant for some given $p \in (1, \infty)$ . We extend this cr…

math.AP2023

The Perron solution for elliptic equations without the maximum principle

W. Arendt, A. F. M. ter Elst, M. Sauter

In this article we consider the Dirichlet problem on a bounded domain $Ω \subset R^{d}$ with respect to a second-order elliptic differential operator in divergence form. We do n…

math.AP2023★ 3 cited

On the convergence of the Willmore flow with Dirichlet boundary conditions

Manuel Schlierf

Very little is yet known regarding the Willmore flow of surfaces with Dirichlet boundary conditions. We consider surfaces with a rotational symmetry as initial data and prove a glo…

math.AP2022

On a kinetic Poincaré inequality and beyond

Lukas Niebel, Rico Zacher

In this article, we give a trajectorial proof of a kinetic Poincaré inequality which plays an important role in the De Giorgi-Nash-Moser theory for kinetic equations. The present w…

math.AP2022★ 6 cited

Statistical solutions of the incompressible Euler equations

Raphael Wagner, Emil Wiedemann

We study statistical solutions of the incompressible Euler equations in two dimensions with vorticity in $L^{p}$ , $1 \leq p \leq \infty$ , and in the class of vortex-sheets with a dist…

math.AP2022★ 3 cited

A dynamic approach to heterogeneous elastic wires

Anna Dall'Acqua, Leonie Langer, Fabian Rupp

We consider closed planar curves with fixed length and arbitrary winding number whose elastic energy depends on an additional density variable and a spontaneous curvature. Working…

math.AP2021★ 4 cited

Kinetic maximal $L_{μ}^{p} (L^{p})$ -regularity for the fractional Kolmogorov equation with variable density

Lukas Niebel

We consider the Kolmogorov equation, where the right-hand side is given by a non-local integro-differential operator comparable to the fractional Laplacian in velocity with possibl…

math.AP2020★ 10 cited

Kinetic maximal $L^{p}$ -regularity with temporal weights and application to quasilinear kinetic diffusion equations

Lukas Niebel, Rico Zacher

We introduce the concept of kinetic maximal $L^{p}$ -regularity with temporal weights and prove that this property is satisfied for the (fractional) Kolmogorov equation. We show that…

math.AP2020★ 11 cited

The volume-preserving Willmore flow

Fabian Rupp

We consider a closed surface in $R^{3}$ evolving by the volume-preserving Willmore flow and prove a lower bound for the existence time of smooth solutions. For spherical ini…

math.AP2020★ 6 cited

Existence and convergence of the length-preserving elastic flow of clamped curves

Fabian Rupp, Adrian Spener

We study the evolution of curves with fixed length and clamped boundary conditions moving by the negative $L^{2}$ -gradient flow of the elastic energy. For any initial curve lying mer…

math.AP2020

Non-Unique Admissible Weak Solutions of the Compressible Euler Equations with Compact Support in Space

Ibrokhimbek Akramov, Emil Wiedemann

This paper is concerned with the existence of compactly supported admissible solutions to the Cauchy problem for the isentropic compressible Euler equations. In more than one space…

math.AP2016★ 3 cited

Removable Singularities of $m$ -Hessian Equations

Hülya Car, René Pröpper

In this paper we give a new, less restrictive condition for removability of singular sets, $E$ , of smooth solutions to the m-Hessian equation (and also for more general fully nonli…

math.AP2010★ 2 cited

The Dirichlet-to-Neumann operator on rough domains

W. Arendt, A. F. M. ter Elst

We consider a bounded connected open set $Ω \subset R^{d}$ whose boundary $Γ$ has a finite $(d - 1)$ -dimensional Hausdorff measure. Then we define the Dirichlet-to-Neumann operato…

math.AP2008

Nonautonomous Kolmogorov parabolic equations with unbounded coefficients

M. Kunze, L. Lorenzi, A. Lunardi

We study a class of elliptic operators $A$ with unbounded coefficients defined in $I\times\CR^d$ for some unbounded interval $I\subset\CR$. We prove that, for any $s \in I$ , the Cau…