Anisotropic nonlinear elliptic systems with measure data and anisotropic harmonic maps into spheres

Abstract

We prove existence results for distributional solutions of anisotropic nonlinear elliptic systems with a measure valued right-hand side. The functional setting involves anisotropic Sobolev spaces as well as weak Lebesgue (Marcinkiewicz) spaces. In a special case we also prove maximal regularity and uniqueness results. Some of the obtained results are applied, along with an anisotropic variant of the div-curl lemma in the Hardy one space, to prove that the space of anisotropic harmonic maps into spheres is compact in the weak topology of the relevant anisotropic Sobolev space.

Keywords

• Elliptic system
• anisotropic
• nonlinear
• measure data
• weak solution
• existence
• harmonic map.