28 citations · 43 across the 14 of their papers we have counts for
17 papers
Fractional higher differentiability of solutions to strongly nonlinear Stokes systems
Andrea Cianchi, Flavia Giannetti, Antonia Passarelli di Napoli +1
This work concerns stationary Stokes type systems governed by a general class of non-necessarily power-type nonlinearities. Fractional regularity properties of the symmetric gradie…
Existence of variational solutions to doubly nonlinear systems in general noncylindrical domains
Leah Schätzler, Christoph Scheven, Jarkko Siltakoski +1
We consider the Cauchy-Dirichlet problem to doubly nonlinear systems of the form \begin{align*} \partial_t \big( |u|^{q-1}u \big) - \operatorname{div} \big( D_ξf(x,u,Du) \big) = -…
Existence of variational solutions to doubly nonlinear systems in nondecreasing domains
Leah Schätzler, Christoph Scheven, Jarkko Siltakoski +1
For , we consider the Cauchy-Dirichlet problem to doubly nonlinear systems of the form \begin{align*} \partial_t \big( |u|^{q-1}u \big) - \operatorname{div} \big…
Higher integrability for singular doubly nonlinear systems
Kristian Moring, Leah Schätzler, Christoph Scheven
We prove a local higher integrability result for the spatial gradient of weak solutions to doubly nonlinear parabolic systems whose prototype is $$ \partial_t \left(|u|^{q-1}u \rig…
Supercaloric functions for the porous medium equation in the fast diffusion case
Kristian Moring, Christoph Scheven
We study a generalized class of supersolutions, so-called supercaloric functions to the porous medium equation in the fast diffusion case. Supercaloric functions are defined as low…
On two notions of solutions to the obstacle problem for the singular porous medium equation
Kristian Moring, Christoph Scheven
We show that two different notions of solutions to the obstacle problem for the porous medium equation, a potential theoretic notion and a notion based on a variational inequality,…
Hölder Continuity of the Gradient of Solutions to Doubly Non-Linear Parabolic Equations
Verena Bögelein, Frank Duzaar, Ugo Gianazza +2
This paper is devoted to studying the local behavior of non-negative weak solutions to the doubly non-linear parabolic equation \begin{equation*} \partial_t u^q - \text{div}\big(|D…
Boundary regularity for parabolic systems in convex domains
Verena Bögelein, Frank Duzaar, Naian Liao +1
In a cylindrical space-time domain with a convex, spatial base, we establish a local Lipschitz estimate for weak solutions to parabolic systems with Uhlenbeck structure up to the l…
On the definition of solution to the total variation flow
Juha Kinnunen, Christoph Scheven
We show that the notions of weak solution to the total variation flow based on the Anzellotti pairing and the variational inequality coincide under some restrictions on the boundar…
Higher integrability in the obstacle problem for the fast diffusion equation
Yumi Cho, Christoph Scheven
We prove local higher integrability of the spatial gradient for solutions to obstacle problems of porous medium type in the fast diffusion case . The result holds for the natu…
Blow-up analysis and boundary regularity for variationally biharmonic maps
Serdar Altuntas, Christoph Scheven
We consider critical points of the bi-energy \[ \int_Ω|Δu|^2\,d x, \] where is a bounded smooth domain of dimension and $N\subset\mathbb{…
Global higher integrability of weak solutions of porous medium systems
Kristian Moring, Christoph Scheven, Sebastian Schwarzacher +1
We establish higher integrability up to the boundary for the gradient of solutions to porous medium type systems, whose model case is given by \begin{equation*} \partial_t u-Δ(|u|^…
Higher integrability for the singular porous medium system
Verena Bögelein, Frank Duzaar, Christoph Scheven
In this paper we establish in the fast diffusion range the higher integrability of the spatial gradient of weak solutions to porous medium systems. The result comes along with an e…
Higher integrability for doubly nonlinear parabolic systems
Verena Bögelein, Frank Duzaar, Juha Kinnunen +1
This paper proves a local higher integrability result for the spatial gradient of weak solutions to doubly nonlinear parabolic systems. The new feature of the argument is that the…
An Anzellotti type pairing for divergence-measure fields and a notion of weakly super--harmonic functions
Christoph Scheven, Thomas Schmidt
We study generalized products of divergence-measure fields and gradient measures of {\rm BV} functions. These products depend on the choice of a representative of the {\rm BV} func…
Minimizers of higher order gauge invariant functionals
Andreas Gastel, Christoph Scheven
We introduce higher order variants of the Yang-Mills functional that involve th order derivatives of the curvature. We prove coercivity and smoothness of critical points in…
The evolution of H-surfaces with a Plateau boundary condition
Frank Duzaar, Christoph Scheven
In this paper we consider the heat flow associated to the classical Plateau problem for surfaces of prescribed mean curvature. We show that an isoperimetric condition on H ensures…