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

Xue Yang; Jing Zhang

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arXiv · 1804.08469

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

Xue Yang·Jing Zhang

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Abstract

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

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Xue Yang, Jing Zhang. 2018-04-23. The Neumann Boundary Problem for Elliptic Partial Differential Equations with Nonlinear Divergence Terms. https://arxiv.org/abs/1804.08469

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