Partial Legendre transforms of non-linear equations
Analysis of PDEs
2010-10-12 v1
Abstract
The partial Legendre transform of a non-linear elliptic differential equation is shown to be another non-linear elliptic differential equation. In particular, the partial Legendre transform of the Monge-Amp\`ere equation is another equation of Monge-Amp\`ere type. In 1+1 dimensions, this can be applied to obtain uniform estimates to all orders for the degenerate Monge-Amp\`ere equation with boundary data satisfying a strict convexity condition.
Keywords
Cite
@article{arxiv.1010.2111,
title = {Partial Legendre transforms of non-linear equations},
author = {Pengfei Guan and D. H. Phong},
journal= {arXiv preprint arXiv:1010.2111},
year = {2010}
}
Comments
12 pages, no figure