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Questions about partial differential equations of elliptic type. Often used in combination with the top-level tag ap.analysis-of-pdes.

3 votes

Gradient estimates

That part of Cheng-Yau's paper is a followup to Yau's paper "Harmonic functions on Riemannian manifolds" from the same year, adapting Yau's work on complete manifolds to geodesic balls. Yau's work is …
Quarto Bendir's user avatar
1 vote
Accepted

A problem of using Schauder estimate in the paper of Yau's proof of calabi conjecture

There are many non-equivalent formulations of the Schauder estimates; the version you are suggesting is the most common. For the version he needs, Yau gives a precise page & theorem reference (p.156, …
Quarto Bendir's user avatar
8 votes
0 answers
249 views

Smoothness of solution map for PDE

I am wondering what sort of results are available for the following sort of problem, or where to look in the literature for work dealing with such problems, especially in the degenerate elliptic conte …
Quarto Bendir's user avatar