Bendahmane, MostafaKarlsen, Kenneth Hvistendahl2021-07-162021-07-162006-04-06Bendahmane, M., & Karlsen, K. H. (2006). Anisotropic nonlinear elliptic systems with measure data and anisotropic harmonic maps into spheres. <i>Electronic Journal of Differential Equations, 2006</i>(46), pp. 1-30.1072-6691https://hdl.handle.net/10877/13919We 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.Text30 pages1 file (.pdf)enAttribution 4.0 InternationalElliptic systemAnisotropicNonlinearMeasure dataWeak solutionExistenceHarmonic mapArticleThis work is licensed under a Creative Commons Attribution 4.0 International License.