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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.

7 votes
2 answers
466 views

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

In http://ams.rice.edu/leavingmsn?url=https://doi.org/10.1524/anly.1996.16.1.101 Prof. Xu-Jia Wang established the boundary estimates for second derivatives of the solution to classical Dirichlet prob …
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1 vote
0 answers
117 views

Degenerate Monge-Ampere equation on a bounded domain with $C^{2,1}$ boundary

In the paper by Guan Pengfei: "C^2 a priori estimates for degenerate Monge-Ampere equations" https://projecteuclid.org/euclid.dmj/1077242669 Prof. P. Guan proved in Theorem 1 that the degenerate Monge …
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