Anisotropic nonlinear elliptic systems with measure data and anisotropic harmonic maps into spheres
Date
2006-04-06
Authors
Bendahmane, Mostafa
Karlsen, Kenneth Hvistendahl
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
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.
Description
Keywords
Elliptic system, Anisotropic, Nonlinear, Measure data, Weak solution, Existence, Harmonic map
Citation
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.
Rights
Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.