Generalized second order vectorial ∞-eigenvalue problems
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 “hi...
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| Published in | Proceedings of the Royal Society of Edinburgh. Section A. Mathematics pp. 1 - 21 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
27.03.2024
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| Online Access | Get full text |
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| Summary: | 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. |
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| ISSN: | 0308-2105 1473-7124 |
| DOI: | 10.1017/prm.2024.27 |