1 results
Generalized second order vectorial ∞-eigenvalue problems
- Part of
-
- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics , First View
- Published online by Cambridge University Press:
- 27 March 2024, pp. 1-21
-
- Article
-
- You have access
- Open access
- HTML
- Export citation
-
We consider the problem of minimizing the $L^\infty$
norm of a function of the hessian over a class of maps, subject to a mass constraint involving the $L^\infty$
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 $L^p$
approximations, we establish the existence of a special $L^\infty$
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.
