Year: 2026
Type: preprint
Abstract: We study an exterior Bernoulli-type free boundary problem associated with the Riemannian $p$-Laplacian on a compact Riemannian manifold. Following the shape-optimization strategy of Ly and Seck, we formulate the corresponding volume-constrained shape optimization problem, derive its first shape derivative, obtain the overdetermined Bernoulli condition through a Lagrange multiplier, and establish a conditional monotonicity result under a Riemannian contraction hypothesis. The final successive-approximation argument will require additional geometric and boundary-flux stability assumptions.
Source: arXiv (Cornell University)
Authors: Djite, Ababacar Sadikhe, Seck, Diaraf
Institution: Cheikh Anta Diop University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7206166570