9 citations · 16 across the 11 of their papers we have counts for
16 papers
A small remark on Bernstein's theorem
Michael Bildhauer, Bernhard Farquhar, Martin Fuchs
We investigate splitting-type variational problems with some linear growth conditions. For balanced solutions of the associated Euler-Lagrange equation we receive a result analogou…
Splitting-type variational problems with asymmetrical growth conditions
Michael Bildhauer, Martin Fuchs
Splitting-type variational problems \[ \int_Ω\sum_{i=1}^n f_i(\partial_i w) dx \to \min \] with superlinear growth conditions are studied by assuming \[ h_i(t) \leq f''_i(t) \leq H…
On the global regularity for minimizers of variational integrals: splitting-type problems in 2D and extensions to the general anisotropic setting
Michael Bildhauer, Martin Fuchs
We mainly discuss superquadratic minimization problems for splitting-type variational integrals on a bounded Lipschitz domain and prove higher integrability…
Small weights in Caccioppoli's inequality and applications to Liouville-type theorems for non-standard problems
Michael Bildhauer, Martin Fuchs
Using a variant of Caccioppoli's inequality involving small weights, i.e. weights of the form for some , we establish several Liouville-type theorem…
An extension of a theorem of Bers and Finn on the removability of isolated singularities to the Euler-Lagrange equations related to general linear growth problems
Michael Bildhauer, Martin Fuchs
A famous theorem of Bers and Finn states that isolated singularities of solutions to the non-parametric minimal surface equation are removable. We show that this result remains val…
Liouville-type results in two dimensions for stationary points of functionals with linear growth
Michael Bildhauer, Martin Fuchs
We consider variational integrals of linear growth satisfying the condition of -ellipticity for some exponent and prove that stationary points : $\mathbb{R}^2 \to \math…
Variational problems of splitting-type with mixed linear-superlinear growth conditions
Michael Bildhauer, Martin Fuchs
Variational problems of splitting-type with mixed linear-superlinear growth conditions are considered. In the twodimensional case the minimizing problem is given by \[ J [w] = \int…
Splitting-type variational problems with linear growth conditions
Michael Bildhauer, Martin Fuchs
Regularity properties of solutions to variational problems are established for a broad class of strictly convex splitting-type energy densities of the principal form : $\mathbb{…
On a class of variational problems with linear growth and radial symmetry
Michael Bildhauer, Martin Fuchs
We discuss variational problems on two-dimensional domains with energy densities of linear growth and with radially symmetric data. The smoothness of generalized minimizers is esta…
Existence results for generalized EED denoising problems
Michael Bildhauer, Martin Fuchs
The joint work of the authors with Marcelo Cárdenas and Joachim Weickert \cite{BCFW:2019_1} on edge-enhancing diffusion inpainting problems leads to the analysis of related denoisi…
Existence Theory for the EED Inpainting Problem
Michael Bildhauer, Marcelo Cárdenas, Martin Fuchs +1
We establish an existence theory for an elliptic boundary value problem in image analysis known as edge-enhancing diffusion (EED) inpainting. The EED inpainting problem aims at res…
A Liouville theorem for stationary incompressible fluids of von Mises type
Martin Fuchs, Jan Mueller
We consider entire solutions of the equations describing the stationary flow of a generalized Newtonian fluid in 2D concentrating on the question, if a Liouville-type result ho…
Convex Regularization of Multi-Channel Images Based on Variants of the TV-Model
Martin Fuchs, Jan Mueller, Christian Tietz +1
We discuss existence and regularity results for multi-channel images in the setting of isotropic and anisotropic variants of the TV-model.
A reciprocity principle for constrained isoperimetric problems and existence of isoperimetric subregions in convex sets
Michael Bildhauer, Martin Fuchs, Jan Mueller
It is a well known fact that in a subset of minimal perimeter among all sets of a given volume is also a set of maximal volume among all sets of the same perimet…
Signal recovery via TV-type energies
Martin Fuchs, Jan Mueller, Christian Tietz
We consider one-dimensional variants of the classical first order total variation denoising model introduced by Rudin, Osher and Fatemi. This study is based on our previous work on…
A higher order TV-type variational problem related to the denoising and inpainting of images
Martin Fuchs, Jan Mueller
We give a comprehensive survey on a class of higher order variational problems which are motivated by applications in mathematical imaging. The overall aim of this note is to inves…