Optimal solvability for a nonlocal problem at critical growth

Lorenzo Brasco (1, 2) , Marco Squassina (3)

1 DMCS - Dipartimento di Matematica e Informatica = Department of Mathematics and Computer Science [Ferrara]
2 I2M - Institut de Mathématiques de Marseille
3 Unicatt - Università cattolica del Sacro Cuore [Brescia]

We provide optimal solvability conditions for a nonlocal minimization problem at critical growth involving an external potential function $a$. Furthermore, we get an existence and uniqueness result for a related nonlocal equation.

Mots clés: Brezis-Nirenberg problem; Critical growth problems; Minimization problems

Domaines: Equations aux dérivées partielles [math.AP]

Lorenzo Brasco, Marco Squassina. Optimal solvability for a nonlocal problem at critical growth. Journal of Differential Equations, 2018, 264 (3), pp.2242-2269. ⟨10.1016/j.jde.2017.10.019⟩. ⟨hal-01559506⟩