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We prove the existence and uniqueness of weak solution of a Neumann boundaryproblem for an elliptic partial differential equation (PDE for short) with asingular divergence term which can only be understood in a weak sense. Aprobabilistic approach is applied by studying the backward stochasticdifferential equation (BSDE for short) corresponding to the PDE.

The Neumann Boundary Problem for Elliptic Partial Differential Equations with Nonlinear Divergence Terms