A Note on Quasilinear Elliptic Systems with L∞-Data - Balaadich, Farah; Azroul, Elhoussine (Eurasian Mathematical Journal, 2023)
Abstract. We prove the existence of a weak energy solution for the boundary value problem $$-\text{div } a(x, u, Du) = f \quad \text{in } Ω,$$ $$u = 0 \quad \text{on } \partial Ω,$$ where \(Ω\) is a smooth bounded open domain in \(\mathbb{R}^n\) (\(n ≥ 3\)) and \(f \in L^∞(Ω; \mathbb{R}^m)\). The existence result is proved using the concept of Young measures.