A Note on Quasilinear Elliptic Systems with L∞-Data

Abstract

Abstract. We prove the existence of a weak energy solution for the boundary value problem

$$-\text{div } a(x, u, Du) = f \quad \text{in } \Omega,$$ $$u = 0 \quad \text{on } \partial \Omega,$$

where \(\Omega\) is a smooth bounded open domain in \(\mathbb{R}^n\) (\(n \geq 3\)) and \(f \in L^\infty(\Omega; \mathbb{R}^m)\). The existence result is proved using the concept of Young measures.