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Asymptotics of nonlocal nonlinear Robin energies
Abstract
We study the free minimization problem for a nonlinear, nonlocal functional associated with Robin-type nonlocal exterior conditions depending on a positive parameter α. We prove that, for every α>0, the minimizer exists, is unique, and satisfies suitable decay properties at infinity. We also investigate the regularity of the maps α↦ uα and α↦ Eα, where~uα denotes the minimizer and Eα the corresponding energy. Finally, we derive asymptotic expansions of the energy as α→+∞ and as α→0+. The latter regime requires distinguishing between two cases, depending on whether the forcing term has zero mass. In one case, the limiting energy possesses a minimizer and Eα converges to its energy, but in the other case Eα diverges to −∞.
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BibTeX
@misc{dipierro2026asymptotics,
title = {{Asymptotics of nonlocal nonlinear Robin energies}},
author = {Serena Dipierro and Giuseppe Spadaro and Enrico Valdinoci},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20692},
eprint = {2609.20692},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20692},
}
RIS
TY - UNPB
TI - Asymptotics of nonlocal nonlinear Robin energies
AU - Serena Dipierro
AU - Giuseppe Spadaro
AU - Enrico Valdinoci
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.20692
UR - https://arxiv.org/abs/2609.20692
AB - We study the free minimization problem for a nonlinear, nonlocal functional associated with Robin-type nonlocal exterior conditions depending on a positive parameter α. We prove that, for every α>0, the minimizer exists, is unique, and satisfies suitable decay properties at infinity. We also investigate the regularity of the maps α↦ u_α and α↦ E_α, where~u_α denotes the minimizer and E_α the corresponding energy. Finally, we derive asymptotic expansions of the energy as α→+∞ and as α→0^+. The latter regime requires distinguishing between two cases, depending on whether the forcing term has zero mass. In one case, the limiting energy possesses a minimizer and E_α converges to its energy, but in the other case E_α diverges to −∞.
ER -