Games for eigenvalues of the Hessian and concave/convex envelopes
We study the PDE λj(D2u)=0, in Ω, with u=g, on ∂Ω. Here λ1(D2u)≤…≤λN(D2u) are the ordered eigenvalues of the Hessian D2u. First, we show a geometric interpretation of the viscosity solutions to the problem in terms of convex/concave envelopes over affine spaces of dimension j. In one of our main res...
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| Formato: | INPR |
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00217824_v_n_p_Blanc |
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todo:paper_00217824_v_n_p_Blanc2023-10-03T14:20:53Z Games for eigenvalues of the Hessian and concave/convex envelopes Blanc, P. Rossi, J.D. Concave/convex envelopes Eigenvalues of the Hessian Games We study the PDE λj(D2u)=0, in Ω, with u=g, on ∂Ω. Here λ1(D2u)≤…≤λN(D2u) are the ordered eigenvalues of the Hessian D2u. First, we show a geometric interpretation of the viscosity solutions to the problem in terms of convex/concave envelopes over affine spaces of dimension j. In one of our main results, we give necessary and sufficient conditions on the domain so that the problem has a continuous solution for every continuous datum g. Next, we introduce a two-player zero-sum game whose values approximate solutions to this PDE problem. © 2018 Elsevier Masson SAS INPR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00217824_v_n_p_Blanc |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Concave/convex envelopes Eigenvalues of the Hessian Games |
| spellingShingle |
Concave/convex envelopes Eigenvalues of the Hessian Games Blanc, P. Rossi, J.D. Games for eigenvalues of the Hessian and concave/convex envelopes |
| topic_facet |
Concave/convex envelopes Eigenvalues of the Hessian Games |
| description |
We study the PDE λj(D2u)=0, in Ω, with u=g, on ∂Ω. Here λ1(D2u)≤…≤λN(D2u) are the ordered eigenvalues of the Hessian D2u. First, we show a geometric interpretation of the viscosity solutions to the problem in terms of convex/concave envelopes over affine spaces of dimension j. In one of our main results, we give necessary and sufficient conditions on the domain so that the problem has a continuous solution for every continuous datum g. Next, we introduce a two-player zero-sum game whose values approximate solutions to this PDE problem. © 2018 Elsevier Masson SAS |
| format |
INPR |
| author |
Blanc, P. Rossi, J.D. |
| author_facet |
Blanc, P. Rossi, J.D. |
| author_sort |
Blanc, P. |
| title |
Games for eigenvalues of the Hessian and concave/convex envelopes |
| title_short |
Games for eigenvalues of the Hessian and concave/convex envelopes |
| title_full |
Games for eigenvalues of the Hessian and concave/convex envelopes |
| title_fullStr |
Games for eigenvalues of the Hessian and concave/convex envelopes |
| title_full_unstemmed |
Games for eigenvalues of the Hessian and concave/convex envelopes |
| title_sort |
games for eigenvalues of the hessian and concave/convex envelopes |
| url |
http://hdl.handle.net/20.500.12110/paper_00217824_v_n_p_Blanc |
| work_keys_str_mv |
AT blancp gamesforeigenvaluesofthehessianandconcaveconvexenvelopes AT rossijd gamesforeigenvaluesofthehessianandconcaveconvexenvelopes |
| _version_ |
1807319499850907648 |