Quasilinear elliptic systems

Abstract

The quasilinear elliptic system {Mathematical expression} 1≤i≤N, x in a bounded domain Ω, and U=0 on the boundary of Ω is studied. Under various assumptions regarding the auxiliary functions C, B, and F, the author studies weak existence, uniqueness, and stability in H01(Ω). In addition, by requiring Cijlm =0 for i ≠ j, it is proved that such weak solutions have bounded L∞(Ω) norm and satisfy a Hölder condition on the closure of Ω. © 1978 Fondazione Annali di Matematica Pura ed Applicata.