Quasilinear elliptic systems under form-bounded coefficients

Abstract

We study quasilinear elliptic systems in divergence form. Under a form-boundedness condition on the nonlinear coefficients, we establish, for sufficiently large damping parameter, the existence and uniqueness of weak solutions in the Sobolev space W¹,ᵖ, with p > l, for right-hand sides in Lᵖ′. The solution is Hölder continuous. Further mild hypotheses guarantee that the solution belongs locally to W²,². The class of admissible coefficients includes singular potentials such as the Coulomb potential, going well beyond classical integrability requirements.