L2, Φ Regularity for Nonlinear Elliptic Systems of Second Order

Abstract

This paper is concerned with the regularity of the gradient of the weak solutions to nonlinear elliptic systems with linear main parts. It demonstrates the connection between the regularity of the (generally discontinuous) coefficients of the linear parts of systems and the regularity of the gradient of the weak solutions of systems. More precisely: If above-mentioned coefficients belong to the class L∞(Ω) ∩ L2,ψ(Ω) (generalized Campanato spaces), then the gradient of the weak solutions belong to L2,Φloc (Ω, ℝnN), where the relation between the functions ψ and Φ is formulated in Theorems 3.1 and 3.2 below.