A stochastic approach to a multivalued Dirichlet-Neumann problem

Lucian Maticiuc and Aurel Rascanu

Stochastic Processes and their Applications, 2010, vol. 120, issue 6, 777-800

Abstract: We prove the existence and uniqueness of a viscosity solution of the parabolic variational inequality (PVI) with a mixed nonlinear multivalued Neumann-Dirichlet boundary condition: where [not partial differential][phi] and [not partial differential][psi] are subdifferential operators and is a second-differential operator given by The result is obtained by a stochastic approach. First we study the following backward stochastic generalized variational inequality: where (At)t>=0 is a continuous one-dimensional increasing measurable process, and then we obtain a Feynman-Kaç representation formula for the viscosity solution of the PVI problem.

Keywords: Variational; inequalities; Backward; stochastic; differential; equations; Neumann-Dirichlet; boundary; conditions; Viscosity; solutions; Feynman-Kac; formula (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (4)

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