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Results tagged with ap.analysis-of-pdes
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user 156492
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
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 …
- 2,247
10
votes
0
answers
408
views
Gromov's compactness theorem via Sacks-Uhlenbeck and Schoen-Uhlenbeck
Gromov's compactness theorem for pseudo-holomorphic curves, in section 1.5 of "Pseudoholomorphic curves in symplectic manifolds," is very well known. I'm aware of the following two proofs:
J.G. Wolfs …
- 2,247
4
votes
0
answers
122
views
Umbilic points of minimal hypersurfaces and distributional Simons inequality
Let $\Sigma$ be a minimal hypersurface of a smooth Riemannian manifold $(M,g)$ with second fundamental form $h$. What can one say about the set $\{p\in\Sigma:h(p)=0\}$? Is each point isolated? (I feel …
- 2,247
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, …
- 2,247
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 …
- 2,247