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On the Large Λ Asymptotics of the One Phase Bernoulli Free Boundary Problem
Abstract
In this paper, we investigate the asymptotic behavior of minimizers uΛ of the Bernoulli functional ∫D |∇ v|2 dx +Λ|Ωv| for large Λ with a boundary datum g ≥ 0. In particular, in the case g>0, we show graphicality of the free boundary over ∂ D and obtain a second order asymptotic expansion in Λ of the graph.
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BibTeX
@misc{siclari2026large,
title = {{On the Large $Λ$ Asymptotics of the One Phase Bernoulli Free Boundary Problem}},
author = {Giovanni Siclari},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12553},
eprint = {2609.12553},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12553},
}
RIS
TY - UNPB
TI - On the Large Λ Asymptotics of the One Phase Bernoulli Free Boundary Problem
AU - Giovanni Siclari
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.12553
UR - https://arxiv.org/abs/2609.12553
AB - In this paper, we investigate the asymptotic behavior of minimizers u_Λ of the Bernoulli functional ∫_D |∇ v|^2 dx +Λ|Ω_v| for large Λ with a boundary datum g ≥ 0. In particular, in the case g>0, we show graphicality of the free boundary over ∂ D and obtain a second order asymptotic expansion in Λ of the graph.
ER -