Mostafa Bendahmane, Kenneth H. Karlsen
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.
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Mostafa Bendahmane Centre of Mathematics for Applications University of Oslo P. O. Box 1053, Blindern, N-0316 Oslo, Norway email: mostafab@math.uio.no |
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Kenneth Hvistendahl Karlsen Centre of Mathematics for Applications University of Oslo P. O. Box 1053, Blindern, N-0316 Oslo, Norway email: kennethk@math.uio.no http://www.math.uio.no/~kennethk/ |
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