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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Detalles Bibliográficos
Publicado: 2018
Materias:
Concave/convex envelopes
Eigenvalues of the Hessian
Games
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00217824_v_n_p_Blanc
http://hdl.handle.net/20.500.12110/paper_00217824_v_n_p_Blanc
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00217824_v_n_p_Blanc
record_format dspace
spelling paper:paper_00217824_v_n_p_Blanc2023-06-08T14:42:06Z Games for eigenvalues of the Hessian and concave/convex envelopes 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 2018 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00217824_v_n_p_Blanc 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
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
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
publishDate 2018
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00217824_v_n_p_Blanc
http://hdl.handle.net/20.500.12110/paper_00217824_v_n_p_Blanc
_version_ 1768541970762825728

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