Anisotropic nonlinear elliptic systems with measure data and anisotropic harmonic maps into spheres
Karlsen, Kenneth Hvistendahl
Texas State University-San Marcos, Department of Mathematics
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.
Elliptic system, Anisotropic, Nonlinear, Measure data, Weak solution, Existence, Harmonic map
Bendahmane, 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.
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