PreprintCC BY 4.0arXiv
Second variation of the fractional torsion energy and linear stability of the ball
Abstract
We compute the second shape derivative of the fractional torsion. It is an explicit quadratic form on the boundary, which involves a Dirichlet-to-Neumann operator for half-harmonic functions blowing up at the boundary. We deduce an explicit formula for volume preserving variations on the ball and show that as in the local case, the shape Hessian is negative and coercive in H1/2 modulo translations.
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BibTeX
@misc{goldman2026second,
title = {{Second variation of the fractional torsion energy and linear stability of the ball}},
author = {Michael Goldman and Matteo Novaga and Berardo Ruffini},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40240},
eprint = {2610.40240},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40240},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Second variation of the fractional torsion energy and linear stability of the ball
AU - Michael Goldman
AU - Matteo Novaga
AU - Berardo Ruffini
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40240
UR - https://arxiv.org/abs/2610.40240
AB - We compute the second shape derivative of the fractional torsion. It is an explicit quadratic form on the boundary, which involves a Dirichlet-to-Neumann operator for half-harmonic functions blowing up at the boundary. We deduce an explicit formula for volume preserving variations on the ball and show that as in the local case, the shape Hessian is negative and coercive in H^1/2 modulo translations.
ER -