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Results tagged with ap.analysis-of-pdes
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user 127803
Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
2
votes
Accepted
Avoidance principle of mean curvature flow for non-compact hypersurfaces?
You can't make such a relaxation, at least in the world of weak set flows. See Example 7.3 (specifically comment iv) of Ilmanen's paper Generalized Flow of Sets by Mean Curvature on a Manifold
I'd be …
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9
votes
1
answer
286
views
Estimate for radius of convergence of solutions given by Cauchy-Kovalevskaya Theorem
I'm sure you can extract it from the proof, but does anyone know of a reference where the radius of convergence (in terms of radius of convergence of the initial data and PDE) of the solution given by …
- 2,478
2
votes
Geometric evolution of convex surfaces to a round sphere
This is a little long for a comment. I also haven't double checked things so may have made mistakes.
I'm going to treat the case of a convex curve in the plane (I imagine something similar works for …
- 2,478
4
votes
Accepted
On the Calabi-Yau conjecture for minimal surfaces
Properness is expected to hold for finite genus embedded minimal surfaces while it seems likely that there are infinite genus counterexamples. Both of these claims are completely open (and are extrem …
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9
votes
Is there a connection between representation theory and PDEs?
Peter Olver has an interesting book on Symmetry and PDEs. Another area to consider (that is particularly important for geometric PDEs) are exterior differential systems. Here are some notes on the s …
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5
votes
Prove Liouville theorem without using mean value property
Here is a more thorough write up of my comment.
Fix a non-negative smooth function $\phi$ which is identically $1$ on $B_1$ and vanishes identically outside $B_2$. Pick $M$ so $|\Delta \phi| \leq M$. …
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1
vote
Distance function to mean curvature flow
This computation is only used when computing the evolution of the function $\phi$ defined on the previous page and $\phi$ is defined so it is supported in a small neighborhood of the smooth solution.
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7
votes
Accepted
Nonsmooth version of Hopf boundary point lemma
I think this is just the comment following Lemma 3.4 of Gilbarg and Trudinger (specifically equation 3.11).
I should add that lowering the regularity of the boundary seems like a harder problem (and i …
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