PreprintCC0arXiv
Uniqueness results for the exterior Dirichlet and Neumann problem in two dimensions for the Euler-Lagrange equations of variational integrals with linear growth
Abstract
We consider solutions u, v:Ω→ℝN of the Euler-Lagrange equations associated to the variational integral ∫Ωf(∇ u)dx, where Ω is an exterior domain in ℝ2 e.g., the complement of a disk or a half plane, and the density f is of linear growth. Among other things we show that u|∂Ω=v|∂Ω together with the boundedness of u−v yields that u=v on the entire domain.
Related
- Bernstein type results for stationary points of variational integrals with subquadratic growth in two dimensions
- Lehto-type growth conditions and a Picard theorem for the gradient of entire solutions to the Euler -- Lagrange equations of variational integrals with linear growth in the plane including a small extension of Moser's Bernstein result
- Regularity for Minimizers of Mixed-Smoothness Variational Integrals
- The Liouville property for entire local minimizers from the space BVloc(R2,RN) of variational integrals with linear growth
- Dirichlet Beta Analogues, Sign Alternation, and Lerch Unification of Hyperbolic and Logarithmic Tangent Integrals
BibTeX
@misc{fuchs2026uniqueness,
title = {{Uniqueness results for the exterior Dirichlet and Neumann problem in two dimensions for the Euler-Lagrange equations of variational integrals with linear growth}},
author = {Michael Bildhauer Martin Fuchs},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01780},
eprint = {2611.01780},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01780},
note = {CC0},
}
RIS
TY - UNPB
TI - Uniqueness results for the exterior Dirichlet and Neumann problem in two dimensions for the Euler-Lagrange equations of variational integrals with linear growth
AU - Michael Bildhauer Martin Fuchs
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01780
UR - https://arxiv.org/abs/2611.01780
AB - We consider solutions u, v:Ω→ℝ^N of the Euler-Lagrange equations associated to the variational integral ∫_Ωf(∇ u)dx, where Ω is an exterior domain in ℝ^2 e.g., the complement of a disk or a half plane, and the density f is of linear growth. Among other things we show that u|_∂Ω=v|_∂Ω together with the boundedness of u−v yields that u=v on the entire domain.
ER -