Geodesic
Optimal regularity in the optimal switching problem
Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 6, pp. 1455-1471.

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In this article we study the optimal regularity for solutions to the following weakly coupled system with interconnected obstacles

{min⁡(−Δu1+f1,u1−u2+ψ1)=0min⁡(−Δu2+f2,u2−u1+ψ2)=0,
arising in the optimal switching problem with two modes.

We derive the optimal C1,1-regularity for the minimal solution under the assumption that the zero loop set L:={ψ1+ψ2=0} is the closure of its interior. This result is optimal and we provide a counterexample showing that the C1,1-regularity does not hold without the assumption L=L0‾.

DOI : 10.1016/j.anihpc.2015.06.001
Keywords: Optimal switching problem, Regularity theory, The obstacle problem, Double obstacle problem, Free boundary problem, Nonlinear elliptic system 
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Aleksanyan, Gohar. Optimal regularity in the optimal switching problem. Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 6, pp. 1455-1471. doi : 10.1016/j.anihpc.2015.06.001. http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2015.06.001/

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