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 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
27.03.2024
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| Online Access | Get full text |
| ISSN | 0308-2105 1473-7124 |
| DOI | 10.1017/prm.2024.27 |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. |
| Author | Katzourakis, Nikos Clark, Ed |
| Author_xml | – sequence: 1 givenname: Ed surname: Clark fullname: Clark, Ed – sequence: 2 givenname: Nikos surname: Katzourakis fullname: Katzourakis, Nikos |
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| Cites_doi | 10.1137/0114053 10.1016/s0294-1449(01)00070-1 10.1051/cocv:2003036 10.1201/9781315195865 10.1512/iumj.1986.35.35003 10.1017/S0308210510000867 10.1007/s00205-018-1305-6 10.1007/s00526-004-0295-4 10.1137/18M1226373 10.1088/1361-6544/ac372a 10.1051/cocv/2014058 10.1007/s00205-003-0278-1 10.1137/13094390X 10.1007/s00526-020-01782-w 10.1515/acv-2016-0052 10.1007/s002050050157 10.1007/978-3-642-61798-0 10.1090/cams/11 10.1007/978-3-319-12829-0 10.1007/s10957-020-01712-y 10.1137/19M1239908 10.1007/s00205-016-1033-8 10.1007/s00245-011-9151-z 10.1016/j.na.2022.112806 10.1080/03605300500299976 10.1006/jmaa.1997.5881 |
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$L^\infty$
norm of a function of the hessian over a class of maps, subject to a mass constraint involving the... |
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