MR3379137 Boualem DJEHICHE, Said HAMADÈNE and Marie-Amelie MORLAIS Boualem DJEHICHE, Said HAMADÈNE and Marie-Amelie MORLAIS Viscosity Solutions of Systems of Variational Inequalities with Interconnected Bilateral Obstacles Funkcialaj Ekvacioj. Serio Internacia 58 2015 134--175 http://fe.math.kobe-u.ac.jp/FE/FullPapers/58-1/58_135.pdf http://www.ams.org/mathscinet-getitem?mr=MR3379137 We study a general class of nonlinear second-order variational inequalities with interconnected bilateral obstacles, related to a multiple modes switching game. Under rather weak assumptions, using systems of penalized unilateral backward SDEs, we construct a continuous viscosity solution of polynomial growth. Moreover, we establish a comparison result which in turn yields uniqueness of the solution. Switching games, variational inequalities, Oblique reflection, Penalization, Backward stochastic differential equation, Bellman-Isaacs equation, Perron's method. 49N70, 49L25, 60H30, 90C39, 93E20. 58-135 2015 Viscosity Solutions of Systems of Variational Inequalities with Interconnected Bilateral Obstacles Boualem DJEHICHE, Said HAMADÈNE and Marie-Amelie MORLAIS Boualem DJEHICHE, Said HAMADÈNE and Marie-Amelie MORLAIS
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