Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 46, pp. 1-30.

Title: Anisotropic nonlinear elliptic  systems  with 
       measure data and  anisotropic harmonic maps into spheres
       
Authors: Mostafa Bendahmane (Univ. of Oslo, Norway)
         Kenneth H. Karlsen (Univ. of Oslo, Norway)

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.

Submitted February 7, 2005. Published April 6, 2006.
Math Subject Classifications: 35A05, 35J70, 58E20.
Key Words: Elliptic system; anisotropic; nonlinear; measure data;
           weak solution; existence; harmonic map.