D-solutions to the system of vectorial calculus of variations in l∞ via the singular value problem

Croce, G., Katzourakis, N. and Pisante, G. (2017) D-solutions to the system of vectorial calculus of variations in l∞ via the singular value problem. Discrete and Continuous Dynamical Systems: Series B, 37 (12). pp. 6165-6181. ISSN 1531-3492 doi: 10.3934/dcds.2017266

Abstract/Summary

For H ∈ C 2 ( R N × n ) and u : Ω ⊆ R n ⟶ R N , consider the system A ∞ u := ( H P ⊗ H P + H [ H P ] ⊥ H P P ) ( D u ) : D 2 u = 0. We construct D -solutions to the Dirichlet problem for (1), an apt notion of generalised solutions recently proposed for fully nonlinear systems. Our D -solutions are W 1 , ∞ -submersions and are obtained without any convexity hypotheses for H , through a result of independent interest involving existence of strong solutions to the singular value problem for general dimensions n ≠ N .

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/71311
Identification Number/DOI	10.3934/dcds.2017266
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	American Institute of Mathematical Sciences
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