Nonlocal elliptic equations with mixed fractional Laplacians: stability and nonexistence results

Résumé

In this study, we investigate the non-existence of solutions to the non-linear elliptic equation involving mixed fractional Laplacians: ( - Δ ) s 1 u + ( - Δ ) s 2 u = | u | p - 1 u in ℝ n , where n ≥ 2 s 1 , 0 < s 2 < s 1 < 1, and p > 1. Here, (−Δ) s denotes the fractional Laplacian in the principal value sense. The presence of two different fractional orders s 1 and s 2 introduces a non-trivial interaction between different diffusive scales, which plays a key role in the analysis. We establish Liouville-type theorems for solutions that are either globally stable or stable outside a compact set. The main techniques employed in our analysis include stability-based integral estimates, a Pohozaev-type identity, and a monotonicity formula.

Citer ce document

Accès au document

Texte intégral en lecture en ligne, réservé aux abonnés SPHAERO et aux membres de l'institution. Se connecter

Auteur(s)

Statistiques

Consultations : 1

Téléchargements : 0