PreprintCC0arXiv
Calabi-Bernstein type theorems for entire solutions of certain nonlinear elliptic equations in the plane
Abstract
We provide some extensions of the classical Calabi-Bernstein theorem to the case of entire solutions of certain nonlinear elliptic equations in two variables. Using an appropriate version of the Calabi correspondence, which formulates a duality between minimal graphs in ℝ3 and maximal spacelike graphs in 𝕃3, our results are a consequence of recent Bernstein type results.
Related
- Liouville theorems and symmetry of positive solutions for partially confined nonlinear Schrödinger equations
- 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
- Gradient estimates and Liouville-type theorems for the semilinear elliptic equation involving the nonlinear gradient source
- Liouville-type theorems and universal estimates for semilinear elliptic equations involving the product of the function and its gradient
- Liouville Theorems for Stable Solutions to Anisotropic Quasilinear Equations
BibTeX
@misc{bildhauer2026calabibernstein,
title = {{Calabi-Bernstein type theorems for entire solutions of certain nonlinear elliptic equations in the plane}},
author = {Michael Bildhauer and Martin Fuchs},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14319},
eprint = {2610.14319},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.14319},
note = {CC0},
}
RIS
TY - UNPB
TI - Calabi-Bernstein type theorems for entire solutions of certain nonlinear elliptic equations in the plane
AU - Michael Bildhauer
AU - Martin Fuchs
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.14319
UR - https://arxiv.org/abs/2610.14319
AB - We provide some extensions of the classical Calabi-Bernstein theorem to the case of entire solutions of certain nonlinear elliptic equations in two variables. Using an appropriate version of the Calabi correspondence, which formulates a duality between minimal graphs in ℝ^3 and maximal spacelike graphs in 𝕃^3, our results are a consequence of recent Bernstein type results.
ER -