# Solving Yamabe Problem by An Iterative Method.

@article{Xu2020SolvingYP, title={Solving Yamabe Problem by An Iterative Method.}, author={Jie Xu}, journal={arXiv: Analysis of PDEs}, year={2020} }

We introduce an iterative scheme to prove the Yamabe problem $ - a\Delta_{g} u + S u = \lambda u^{p-1} $, firstly on open domain $ (\Omega, g) $ with Dirichlet boundary conditions, and then on closed manifolds $ (M, g) $ by local argument. It is a new proof, which solves the Yamabe problem for $ n \geqslant 3 $ in a uniform argument, beyonds the traditional analysis with respect to the minimization of functionals.

#### References

SHOWING 1-10 OF 11 REFERENCES

Global Analysis of Quasilinear Wave Equations on Asymptotically Kerr-de Sitter Spaces

- Mathematics
- 2016

A rapidly convergent iteration method and non-linear partial differential equations - I

- Mathematics
- 1966