Corpus ID: 220042263

# Iterative Methods for Globally Lipschitz Nonlinear Laplace Equations

@article{Xu2019IterativeMF,
title={Iterative Methods for Globally Lipschitz Nonlinear Laplace Equations},
author={Jie Xu},
journal={arXiv: Analysis of PDEs},
year={2019}
}
• Jie Xu
• Published 2019
• Physics
• arXiv: Analysis of PDEs
We introduce an iterative method to prove the existence and uniqueness of the complex-valued nonlinear elliptic PDE of the form $-\Delta u + F(u) = f$ with Dirichlet or Neumann boundary conditions on a precompact domain $\Omega \subset \mathbb{R}^{n}$, where $F : \mathbb{C} \rightarrow \mathbb{C}$ is Lipschitz. The same method gives a solution to $- \Delta_{g} u + F(u) = f$ for these boundary conditions on a smooth, compact Riemannian manifold $(M, g)$ with $\mathcal{C}^{1}$ boundary… Expand
1 Citations

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