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<p>Based on probabilistic methods, we discuss the relationship between viscosity and distribution solutions for semi-linear partial differential equations (PDEs) with Neumann boundary conditions. We also extend the research to a type of nonlinear PDEs, which is completed through the well-posedness and continuity results of solutions to the corresponding forward-backward SDE.</p>

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On the Relationship Between Viscosity and Distribution Solutions for Nonlinear Neumann Type PDEs: The Probabilistic Approach

  • 期刊论文

  • 发表日期：

    2025年1月18日

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  • Jiagang Ren,
  • Shoutian Wang,
  • Jing Wu

摘要

Based on probabilistic methods, we discuss the relationship between viscosity and distribution solutions for semi-linear partial differential equations (PDEs) with Neumann boundary conditions. We also extend the research to a type of nonlinear PDEs, which is completed through the well-posedness and continuity results of solutions to the corresponding forward-backward SDE.