Bernstein type results for stationary points of variational integrals with subquadratic growth in two dimensions
Year: 2026
Type: preprint
Abstract: We discuss entire solutions $u \in C^2(\mathbb{R}^2)$ of the equation ${\rm div}(\nabla f(\nabla u)) = 0$ with strictly convex density $f: \mathbb{R}^2 \rightarrow \mathbb{R}$ of subquadratic growth and prove that $u$ is an affine function provided that at least one partial derivative is bounded from one side. Further results concern the behaviour of non-affine entire solutions.
Source: arXiv (Cornell University)
Authors: Bildhauer, Michael, Fuchs, Martin
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214126681