PreprintCC BY-NC-SA 4.0arXiv
The Calderón Problem for Quasilinear Currents
Abstract
We study the Calderón problem for smooth quasilinear current laws on a bounded domain in ℝn, n≥3. Under the stated structural assumptions and analyticity conditions, the interior current law is determined by local Dirichlet-to-Neumann maps, up to a partial-boundary-fixing diffeomorphism and a Hall-effect-type invisible current. The two obstructions come from the linearized inverse problem, which is solved by combining boundary determination for magnetic Schrödinger operators with analytic continuation in solution coordinates. Higher-order linearization and a boundary argument involving products of three solution gradients then determine the remaining Taylor coefficients.
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BibTeX
@misc{jin2026calderón,
title = {{The Calderón Problem for Quasilinear Currents}},
author = {Ziyun Jin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25337},
eprint = {2610.25337},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25337},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - The Calderón Problem for Quasilinear Currents
AU - Ziyun Jin
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.25337
UR - https://arxiv.org/abs/2610.25337
AB - We study the Calderón problem for smooth quasilinear current laws on a bounded domain in ℝ^n, n≥3. Under the stated structural assumptions and analyticity conditions, the interior current law is determined by local Dirichlet-to-Neumann maps, up to a partial-boundary-fixing diffeomorphism and a Hall-effect-type invisible current. The two obstructions come from the linearized inverse problem, which is solved by combining boundary determination for magnetic Schrödinger operators with analytic continuation in solution coordinates. Higher-order linearization and a boundary argument involving products of three solution gradients then determine the remaining Taylor coefficients.
ER -