3:00 pm Friday, April 20, 2018
Junior Analysis: The two membranes problem for fully nonlinear operators. by Hernan Vivas in 11.176
The two membranes problem was first studied by Vergara-Caffarelli in the context of variational inequalities to study the equilibrium position of two elastic membranes that are prescribed to remain one on top of the other and are not allowed to cross. In the linear elliptic case the problem can be reduced to the classical obstacle problem by considering the vertical distance between the two membranes. The nonlinear case in divergence form was studied by Silvestre in '05 where the situation can, again, be reduced to an obstacle type problem for the difference of the two functions. In a recent paper, Caffarelli, De Silva and Savin considered the two membranes problem for two different (possibly nonlocal) operators with not necessarily the same order. In this talk, motivated by a model in mathematical finance, we will consider the two membranes problem for two fully nonlinear operators satisfying a type of compatibility condition. Submitted by
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