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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…
Some geometric properties of nonparametric -surfaces in
Michael Bildhauer, Matin Fuchs
Smooth solutions of the equation \[ \rm{div}\, \Bigg\{ \frac{g'\big(|\nabla u|\big)}{|\nabla u|} \nabla u \Bigg\} = 0 \] are considered generating nonparametric -surfaces in $\m…
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{…