PreprintCC BY 4.0arXiv
Bernstein type results for stationary points of variational integrals with subquadratic growth in two dimensions
Abstract
We discuss entire solutions u ∈ C2(ℝ2) of the equation div(∇ f(∇ u)) = 0 with strictly convex density f: ℝ2 → 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.
Related
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BibTeX
@misc{bildhauer2026bernstein,
title = {{Bernstein type results for stationary points of variational integrals with subquadratic growth in two dimensions}},
author = {Michael Bildhauer and Martin Fuchs},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26074},
eprint = {2609.26074},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26074},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Bernstein type results for stationary points of variational integrals with subquadratic growth in two dimensions
AU - Michael Bildhauer
AU - Martin Fuchs
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.26074
UR - https://arxiv.org/abs/2609.26074
AB - We discuss entire solutions u ∈ C^2(ℝ^2) of the equation div(∇ f(∇ u)) = 0 with strictly convex density f: ℝ^2 → 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.
ER -