Regularizing effect for some p-Laplacian systems. (November 2019)

• Record Type: Journal Article
• Authors: Durastanti, Riccardo
• Is Part Of: Nonlinear analysis. Volume 188(2019)
• Page Start: 425
• Page End: 438
• Publication Date: 2019-11
• Subjects: 35J47 -- 35J50 -- 35J60; Nonlinear elliptic systems -- Schrödinger–Maxwell equations -- Variational methods; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.06.011
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study existence and regularity of weak solutions for the following p -Laplacian system − Δ p u + A φ θ + 1 | u | r − 2 u = f, u ∈ W 0 1, p ( Ω ), − Δ p φ = | u | r φ θ, φ ∈ W 0 1, p ( Ω ), where Ω is an open bounded subset of R N ( N ≥ 2 ), Δ p v ≔ div ( | ∇ v | p − 2 ∇ v ) is the p -Laplacian operator, for 1 < p < N, A > 0, r > 1, 0 ≤ θ < p − 1 and f belongs to a suitable Lebesgue space. In particular, we show how the coupling between the equations in the system gives rise to a regularizing effect producing the existence of finite energy solutions.