Artículo
Blanc, P.; Rossi, J.D. "Games for eigenvalues of the Hessian and concave/convex envelopes" (2018) Journal des Mathematiques Pures et Appliquees
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Abstract:
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
Registro:
| Documento: | Artículo |
| Título: | Games for eigenvalues of the Hessian and concave/convex envelopes |
| Autor: | Blanc, P.; Rossi, J.D. |
| Filiación: | Departamento de Matemática, FCEyN, Universidad de Buenos Aires, IMAS – CONICET, Pabellón I, Ciudad Universitaria (1428), Buenos Aires, Argentina |
| Palabras clave: | Concave/convex envelopes; Eigenvalues of the Hessian; Games |
| Año: | 2018 |
| DOI: | http://dx.doi.org/10.1016/j.matpur.2018.08.007 |
| Título revista: | Journal des Mathematiques Pures et Appliquees |
| Título revista abreviado: | J. Math. Pures Appl. |
| ISSN: | 00217824 |
| CODEN: | JMPAA |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00217824_v_n_p_Blanc |
Citas:
---------- APA ----------
Blanc, P. & Rossi, J.D. (2018) . Games for eigenvalues of the Hessian and concave/convex envelopes. Journal des Mathematiques Pures et Appliquees.http://dx.doi.org/10.1016/j.matpur.2018.08.007
---------- CHICAGO ----------
Blanc, P., Rossi, J.D. "Games for eigenvalues of the Hessian and concave/convex envelopes" . Journal des Mathematiques Pures et Appliquees (2018).http://dx.doi.org/10.1016/j.matpur.2018.08.007
---------- MLA ----------
Blanc, P., Rossi, J.D. "Games for eigenvalues of the Hessian and concave/convex envelopes" . Journal des Mathematiques Pures et Appliquees, 2018.http://dx.doi.org/10.1016/j.matpur.2018.08.007
---------- VANCOUVER ----------
Blanc, P., Rossi, J.D. Games for eigenvalues of the Hessian and concave/convex envelopes. J. Math. Pures Appl. 2018.http://dx.doi.org/10.1016/j.matpur.2018.08.007
