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
Solving Yamabe Problem by An Iterative Method.

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