Non-local diffusions, drifts and games

Nonlinear Partial Differential Equations: The Abel Symposium 2010

Volumn , Issue , 2012, Pages 37-52

  Caffarelli, Luis ^a  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFUSIVE PROCESS; LAPLACIAN MODEL; NON-LINEAR ELLIPTIC EQUATION; NONLOCAL DIFFUSION; OPTIMAL CONTROLS; PROPERTIES OF SOLUTIONS; REGULAR SOLUTION; VARIATIONAL STRUCTURES;

CONTINUUM MECHANICS; CONTROL; GAME THEORY; PARTIAL DIFFERENTIAL EQUATIONS; POPULATION DYNAMICS; POROUS MATERIALS;

NONLINEAR EQUATIONS;

EID: 84867962044     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1007/978-3-642-25361-4_3     Document Type: Conference Paper

References (17)

1. Barlow, M.T., Bass, R.F., Chen, Zh.Q., Kassmann, M.: Non-local Dirichlet forms and symmetric jump processes. Trans. Am. Math. Soc. 361(4), 1963-1999 (2009)
2. Bjorland, C, Caffarelli, L., Figalli, A.: Non-local tug-of-war and the infinity fractional Laplacian. arXiv:1011.1966
3. Bass, R.F., Kassmann, M.: Harnack inequalities for non-local operators of variable order. Trans. Am. Math. Soc. 357(2), 837-850 (2005)
4. Caffarelli, L., Cabre, X.: Fully Nonlinear Elliptic Equations. Am. Math. Soc. Colloq. Publ., Vol. 43. Am. Math. Soc, Providence (1995)
5. Caffarelli, L., Vasseur, A.: Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation. Ann. Math. (2011, in press)
6. Caffarelli, L.A., Silvestre, L.: Regularity theory for fully nonlinear integro-differential equations. Commun. Pure Appl. Math. 62(5), 597-638 (2009)
7. Caffarelli, L.A., Silvestre, L.: Regularity results for nonlocal equations by approximation. Arch. Ration. Mech. Anal. (2011, in press). arXiv:0902.4030
8. Caffarelli, L.A., Silvestre, L.: The Evans-Krylov theorem for non local fully non linear equations. Ann. Math. (2011, in press). arXiv:0905.1339
9. Caffarelli, L.A., Chan, C.H., Vasseur, A.: Regularity theory for nonlinear integral operators. arXiv:1003.1699
10. Chambolle, A., Lindgren, E., Monneau, R.: The Hölder infinite Laplacian and Hölder extensions. Preprint (2010)
11. Duvant, G., Lions, J.-L.: Les inéquations en mécanique et en physique. Travaux et Recherches Mathématiques, Vol. 21. Dunod, Paris (1972) (in French)
12. Giacomin, G., Lebowitz, J.L., Presutti, E.: Deterministic and stochastic hydrodynamic equations arising from simple microscopic model systems. In: Stochastic Partial Differential Equations: Six Perspectives. Math. Surveys Monogr., Vol. 64, pp. 107-152. Am. Math. Soc, Providence (1999)
13. Gilboa, G, Osher, S.: Nonlocal operators with applications to image processing. Multiscale Model. Simul. 7(3), 1005-1028 (2008)
14. Kassmann, M.: A priori estimates for integro-differential operators with measurable kernels. Calc Var. Partial Differ. Equ. 34(1), 1-21 (2009)
15. Komatsu, T: Uniform estimates for fundamental solutions associated with non-local Dirichlet forms. Osaka J. Math. 32(4), 833-860 (1995)
16. Peres, Y., Sheffield, S.: Tug-of-war with noise: a game-theoretic view of the p-Laplacian. Duke Math. J. 145(1), 91-120 (2008)
17. Peres, Y., Schramm, O., Sheffield, S., Wilson, D.B.: Tug-of-war and the infinity Laplacian. J. Am. Math. Soc. 22(1), 167-210 (2009)