Regularity theory for the Isaacs equation through approximation methods
Annales de l'I.H.P. Analyse non linéaire, Tome 36 (2019) no. 1, pp. 53-74.
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In this paper, we propose an approximation method to study the regularity of solutions to the Isaacs equation. This class of problems plays a paramount role in the regularity theory for fully nonlinear elliptic equations. First, it is a model-problem of a non-convex operator. In addition, the usual mechanisms to access regularity of solutions fall short in addressing these equations. We approximate an Isaacs equation by a Bellman one, and make assumptions on the latter to recover information for the former. Our techniques produce results in Sobolev and Hölder spaces; we also examine a few consequences of our main findings.

DOI : 10.1016/j.anihpc.2018.03.010
Classification : 35B65, 35J60, 35Q91
Mots-clés : Isaacs equations, Regularity theory, Estimates in Sobolev and Hölder spaces, Approximation methods 
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Pimentel, Edgard A. Regularity theory for the Isaacs equation through approximation methods. Annales de l'I.H.P. Analyse non linéaire, Tome 36 (2019) no. 1, pp. 53-74. doi : 10.1016/j.anihpc.2018.03.010. http://archive.numdam.org/articles/10.1016/j.anihpc.2018.03.010/

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