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