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
Autores principales: Blanc, P., Rossi, J.D.
Formato: INPR
Materias:
Concave/convex envelopes
Eigenvalues of the Hessian
Games
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00217824_v_n_p_Blanc
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
Descripción
Sumario: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

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