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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| Autores principales: | , |
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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 |
| Aporte de: |
| 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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