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arXiv · 2609.26074

Bernstein type results for stationary points of variational integrals with subquadratic growth in two dimensions

Michael Bildhauer·Martin Fuchs
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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.

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Michael Bildhauer, Martin Fuchs. 2026-08-02. Bernstein type results for stationary points of variational integrals with subquadratic growth in two dimensions. https://arxiv.org/abs/2609.26074

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