{"ID":23638583,"CreatedAt":"2026-09-18T07:21:59.209084423Z","UpdatedAt":"2026-09-18T07:21:59.209084423Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.20692","arxiv_id":"2609.20692","title":"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 $α\u003e0$, 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 $-\\infty$.","short_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 $α\u003e0$, the minimizer exists, is unique, and satisfies suitable decay properties at infinity. We also investigate the regular...","url_abs":"https://arxiv.org/abs/2609.20692","url_pdf":"https://arxiv.org/pdf/2609.20692v1","authors":"[\"Serena Dipierro\",\"Giuseppe Spadaro\",\"Enrico Valdinoci\"]","published":"2026-09-17T16:58:20Z","proceeding":"math.AP","tasks":"[\"math.AP\"]","methods":"[]","has_code":false}