Shape Optimization and Bernoulli Free Boundary Problems for the Riemannian $p$-Laplacian

Ababacar Sadikhe Djite; Diaraf Seck

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arXiv · 2609.00571

Shape Optimization and Bernoulli Free Boundary Problems for the Riemannian $p$-Laplacian

Ababacar Sadikhe Djite·Diaraf Seck

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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.

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Ababacar Sadikhe Djite, Diaraf Seck. 2026-09-11. Shape Optimization and Bernoulli Free Boundary Problems for the Riemannian $p$-Laplacian. https://arxiv.org/abs/2609.00571

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