Artículo
Manfredi, J.J.; Rossi, J.D.; Somersille, S.J. "An obstacle problem for tug-of-war games" (2015) Communications on Pure and Applied Analysis. 14(1):217-228
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Abstract:
We consider the obstacle problem for the infinity Laplace equation. Given a Lipschitz boundary function and a Lipschitz obstacle we prove the existence and uniqueness of a super infinity-harmonic function constrained to lie above the obstacle which is infinity harmonic where it lies strictly above the obstacle. Moreover, we show that this function is the limit of value functions of a game we call obstacle tug-of-war.
Registro:
| Documento: | Artículo |
| Título: | An obstacle problem for tug-of-war games |
| Autor: | Manfredi, J.J.; Rossi, J.D.; Somersille, S.J. |
| Filiación: | Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, United States Departamento de Análisis Matemático, Universidad de Alicante, Ap 99, Alicante, 03080, Spain Departamento de Matemática, FCEyN Universidad de Buenos Aires, Ciudad Universitaria, Pab 1, Buenos Aires, 1428, Argentina Department of Mathematics, Dartmouth College, Hanover, NH 03755, United States |
| Palabras clave: | Infinity laplacian; Obstacle problem; Tug-of-war games |
| Año: | 2015 |
| Volumen: | 14 |
| Número: | 1 |
| Página de inicio: | 217 |
| Página de fin: | 228 |
| DOI: | http://dx.doi.org/10.3934/cpaa.2015.14.217 |
| Título revista: | Communications on Pure and Applied Analysis |
| Título revista abreviado: | Commun. Pure Appl. Anal. |
| ISSN: | 15340392 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15340392_v14_n1_p217_Manfredi |
Referencias:
- Antunović, T., Peres, Y., Sheffieeld, S., Somersille, S., Tug-of-war and infinity Laplace equation with vanishing Neumann boundary conditions (2012) Communications in Partial Differential Equations, 37, pp. 1839-1869
- Armstrong, S.N., Smart, C.K., Somersille, S.J., An infinity Laplace equation with gradient term and mixed boundary conditions (2011) Proc. Amer. Math. Soc., 139, pp. 1763-1776
- Aronsson, G., Crandall, M.G., Juutinen, P., A tour of the theory of absolutely minimizing functions (2004) Bull. Amer. Math. Soc., 41, pp. 439-505
- Bhattacharya, T., Di Benedetto, E., Manfredi, J., Limits as p → ∞ of Δpup = f and related extremal problems (1991) Rend. Sem. Mat. Univ. Politec. Torino, pp. 15-68
- Bjorland, C., Caffarelli, L., Figalli, A., Non-local tug-of-war and the infinity fractional Laplacian (2012) Comm. Pure. Appl. Math., 65, pp. 337-380
- Caselles, V., Morel, J.M., Sbert, C., An axiomatic approach to image interpolation (1998) IEEE Trans. Image Process, 7, pp. 376-386
- Crandall, M.G., Ishii, H., Lions, P.L., User's guide to viscosity solutions of second order partial differential equations (1992) Bull. Amer. Math. Soc., 27, pp. 1-67
- Maitra, A.P., Sudderth, W.D., Discrete gambling and stochastic games (1996) Applications of Mathematics, 32. , Springer-Verlag
- Manfredi, J.J., Parviainen, M., Rossi, J.D., An asymptotic mean value characterization of p-harmonic functions (2010) Proc. Amer. Math. Soc., 138, pp. 881-889
- Manfredi, J.J., Parviainen, M., Rossi, J.D., Dynamic programming principle for tug-of-war games with noise (2012) Control Optim. Calc. Var. COCV, 18, pp. 81-90
- Manfredi, J.J., Parviainen, M., Rossi, J.D., On the definition and properties of p-harmonious functions (2012) Annali Scuola Normale Sup. Pisa, Clase di Scienze, 11, pp. 215-241
- Manfredi, J.J., Parviainen, M., Rossi, J.D., An asymptotic mean value characterization for a class of nonlinear parabolic equations related to tug-of-war games (2010) SIAM J. Math. Anal., 42, pp. 2058-2081
- Peres, Y., Pete, G., Somersille, S., Biased tug-of-war, the biased infinity Laplacian and comparison with exponential cones (2010) Calc. Var. Partial Differential Equations, 38, pp. 541-564
- Peres, Y., Schramm, O., Sheffield, S., Wilson, D., Tug-of-war and the infinity Laplacian (2009) J. Amer. Math. Soc., 22, pp. 167-210
- Peres, Y., Sheffield, S., Tug-of-war with noise: A game theoretic view of the p-Laplacian (2008) Duke Math. J., 145, pp. 91-120
- Rossi, J.D., Teixeira, E.V., Urbano, J.M., Optimal Regularity at the Free Boundary for the Infinity Obstacle Problem, , Preprint
Citas:
---------- APA ----------
Manfredi, J.J., Rossi, J.D. & Somersille, S.J. (2015) . An obstacle problem for tug-of-war games. Communications on Pure and Applied Analysis, 14(1), 217-228.http://dx.doi.org/10.3934/cpaa.2015.14.217
---------- CHICAGO ----------
Manfredi, J.J., Rossi, J.D., Somersille, S.J. "An obstacle problem for tug-of-war games" . Communications on Pure and Applied Analysis 14, no. 1 (2015) : 217-228.http://dx.doi.org/10.3934/cpaa.2015.14.217
---------- MLA ----------
Manfredi, J.J., Rossi, J.D., Somersille, S.J. "An obstacle problem for tug-of-war games" . Communications on Pure and Applied Analysis, vol. 14, no. 1, 2015, pp. 217-228.http://dx.doi.org/10.3934/cpaa.2015.14.217
---------- VANCOUVER ----------
Manfredi, J.J., Rossi, J.D., Somersille, S.J. An obstacle problem for tug-of-war games. Commun. Pure Appl. Anal. 2015;14(1):217-228.http://dx.doi.org/10.3934/cpaa.2015.14.217
