Details

Autor(en) / Beteiligte

• de Albuquerque, J. C.
• de Assis, L. R. S.
• Carvalho, M. L. M.
• Salort, A.

Titel

On Fractional Musielak–Sobolev Spaces and Applications to Nonlocal Problems

Ist Teil von

• The Journal of geometric analysis, 2023-04, Vol.33 (4), Article 130

Ort / Verlag

New York: Springer US

Erscheinungsjahr

2023

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• In this work, we establish some abstract results on the perspective of the fractional Musielak–Sobolev spaces, such as: uniform convexity, Radon–Riesz property with respect to the modular function, ( S + ) -property, Brezis–Lieb type Lemma to the modular function and monotonicity results. Moreover, we apply the theory developed to study the existence of solutions to the following class of nonlocal problems ( - Δ ) Φ x , y s u = f ( x , u ) , in Ω , u = 0 , on R N \ Ω , where N ≥ 2 , Ω ⊂ R N is a bounded domain with Lipschitz boundary ∂ Ω and f : Ω × R → R is a Carathéodory function not necessarily satisfying the Ambrosetti–Rabinowitz condition. Such class of problems enables the presence of many particular operators, for instance, the fractional operator with variable exponent, double-phase and double-phase with variable exponent operators, anisotropic fractional p -Laplacian, among others.