Year: 2026
Type: preprint
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 $α\mapsto u_α$ and $α\mapsto E_α$, where~$u_α$ denotes the minimizer and $E_α$ the corresponding energy. Finally, we derive asymptotic expansions of the energy as $α\to+\infty$ and as $α\to0^+$. 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 $-\infty$.
Source: arXiv (Cornell University)
Institutions: The University of Western Australia, University of Calabria
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G1403924678
OpenAlex ID: W7213578734