Author

M. Bildhauer

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Preprint Oct 2026

Giaquinta's example revisited: the Liouville property for a class of nonuniformly elliptic equations in low dimensions

We consider entire solutions $u$: $\mathbb{R}^n \rightarrow \mathbb{R}$, $n \ge 2$, of the equation $\operatorname{div}(\nabla f(\nabla u)) = 0$ with convex density $f$: $\mathbb{R}^n \rightarrow \mathbb{R}$ given for example by $f(\nabla u) = \sum_{i=1}^n |\partial_i u|^{p_i}$ with exponents $p_i \ge 2$ including Giaq...

M. Bildhauer, M. Fuchs · 0 citations

Preprint Aug 2026

Bernstein's theorem for variational integrals of linear growth and radial structure

We consider entire solutions $u: \mathbb{R}^2 \rightarrow \mathbb{R}$ of the Euler-Lagrange equation associated to the variational integral $\int_{\Omega} g(|\nabla u|)\,dx$ with a strictly convex density $g: [0,\infty)\rightarrow \mathbb{R}$ being of linear growth. We show that the condition $\int_{0}^{\infty} t\,g''(...

M. Fuchs, M. Bildhauer · 0 citations

Preprint Aug 2026

Uniqueness and boundary behaviour of solutions to variational problems with linear growth

We investigate the Dirichlet problem for the variational integral $J[u] = \int_{\Omega} f(\nabla u) \, dx$ with density $f$ of linear growth satisfying appropriate ellipticity conditions. We show that the relaxed problem admits a unique solution $u$ in the space of functions of bounded variation, if the set $\Gamma_0$...

M. Bildhauer, M. Fuchs · 0 citations