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Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.

3 votes

A question on the Evans-Krylov theorem and regularity of Monge-Ampere equation

I just want to add and mention the wonderful results by O.Savin in paper "Pointwise $C^{2,\alpha}$ estimates at the boundary for the Monge-Ampère equation.J. Amer. Math. Soc. 26 (2013)", which improve …
John Sung's user avatar
  • 111
3 votes

Question on PDEs which are related to certain geometric problems (e.g. Calabi conjecture, Ga...

For operator f(\lambda)=\log P_k(\lambda), in Guan Bo's several papers, say arXiv:1409.3633v1, Page 5 below Theorem 1.9, they mention some basic properties about it, such as it satisfies (1.2) to (1.6 …
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  • 111