Abstract:We study the stability of $p$-area minimizing surfaces in the Heisenberg group under perturbations of the weight function and the drift vector field in generalized least gradient problems of the form \[ \inf_{w\in BV_0(\Omega)} \int_\Omega \left(a(x)|Dw+F(x)|+H(x)w\right)\,dx. \] Owing to the lack of strict convexity, establishing stability of minimizers is challenging. We derive quantitative stability estimates for minimizers. In particular, under suitable nondegeneracy and geometric assumptions, we obtain $L^1$ and $W^{1,1}$ stability estimates with respect to perturbations of the weight function $a$ and the drift vector field $F$. We further establish unified quantitative stability estimates under simultaneous perturbations of all principal parameters, namely $a$, $F$, and $H$. Numerical simulations illustrating the stability theory are also presented.
| Subjects: | Analysis of PDEs (math.AP) |
| Cite as: | arXiv:2605.24317 [math.AP] |
| (or arXiv:2605.24317v1 [math.AP] for this version) | |
| https://doi.org/10.48550/arXiv.2605.24317 arXiv-issued DOI via DataCite (pending registration) |
From: Amir Moradifam [view email]
[v1]
Sat, 23 May 2026 00:51:08 UTC (426 KB)
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