Quasilinear elliptic systems with nonlinear physical data

Abstract

Using the theory of Young measures, we prove the existence of weak solutions to the following quasilinear elliptic system: A(u)=f(x)+div σ0(x,u), where A(u)=−div σ(x,u,Du) and f∈W−1LM¯(Ω;ℝm). This problem corresponds to a diffusion phenomenon with a source f in a moving and dissolving substance, where the motion is described by σ0.