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Results tagged with calculus-of-variations
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user 1540
Questions on the calculus of variations, which deals with the optimization of functionals mostly defined on infinite dimensional spaces.
2
votes
How to find critical points of functionals when there is a boundary?
The boundary case works without any major change (at least for a reasonable functional). For example, if you consider the Allen--Cahn energy $E_\epsilon$ and take $W^{1,2}(M)$ then critical points of …
- 6,992
2
votes
Symmetry Properties of Minimizers - Calculus of Variations
Here is an explicit example, which may or may not fit into your requirements:
In http://www.ams.org/mathscinet-getitem?mr=308905, "The equivariant Plateau problem and interior regularity," Lawson sho …
- 6,992
6
votes
Variation of curvature with respect to immersion?
One nice source for such computations is contained in the following notes of Schnurer: https://www2.math.hu-berlin.de/gradkoll/Schnuerer_alpbach%5B1%5D.pdf, Section 3.
To be pedantic, technically the …
- 6,992
6
votes
Accepted
Given an eigenvalue equation (elliptic PDE) in a ball $B_R$, prove the convergence of the fi...
For simplicity let me take $H$ smooth or at least $C^\alpha$ so that I don't have to worry about elliptic estimates:
Limit as $R\to\infty$:
Use
$$
\lambda_R = \inf_{\phi \in C^\infty_c(B_R)}\frac{\i …
- 6,992
5
votes
Accepted
Survey paper on isoperimetry
There's been several articles in the comments that are "historical survey" articles. Its not totally clear if you're interested in "current research surveys," but if you are, here are several very ni …
- 6,992
6
votes
Accepted
What is the current status on bad tangent cones at isolated singularities?
(i) This used to be a wide open area, but recently there has been some progress: Gabor Székelyhidi has constructed an example of an isolated singularity with a cylindrical tangent cone here: https://a …
- 6,992