Generalized second order vectorial ∞-eigenvalue problems

Clark, E. and Katzourakis, N. (2024) Generalized second order vectorial ∞-eigenvalue problems. Proceedings of the Royal Society of Edinburgh A: Mathematics. ISSN 1473-7124 doi: 10.1017/prm.2024.27

Abstract/Summary

We consider the problem of minimizing the L∞ norm of a function of the hessian over a class of maps, subject to a mass constraint involving the L∞ norm of a function of the gradient and the map itself. We assume zeroth and first order Dirichlet boundary data, corresponding to the “hinged” and the “clamped” cases. By employing the method of Lp approximations, we establish the existence of a special L∞ minimizer, which solves a divergence PDE system with measure coefficients as parameters. This is a counterpart of the Aronsson-Euler system corresponding to this constrained variational problem. Furthermore, we establish upper and lower bounds for the eigenvalue.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/119241
Identification Number/DOI	10.1017/prm.2024.27
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Cambridge University Press
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