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PreprintCC BY 4.0arXiv

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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Cite

BibTeXRIS
BibTeX
@misc{djite2026shape,
  title = {{Shape Optimization and Bernoulli Free Boundary Problems for the Riemannian $p$-Laplacian}},
  author = {Ababacar Sadikhe Djite and Diaraf Seck},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.00571},
  eprint = {2609.00571},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.00571},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Shape Optimization and Bernoulli Free Boundary Problems for the Riemannian p-Laplacian
AU  - Ababacar Sadikhe Djite
AU  - Diaraf Seck
PY  - 2026
DA  - 2026/09/11
PB  - arXiv
DO  - 10.48550/arxiv.2609.00571
UR  - https://arxiv.org/abs/2609.00571
AB  - 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.
ER  -