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Results tagged with calculus-of-variations
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user 4354
Questions on the calculus of variations, which deals with the optimization of functionals mostly defined on infinite dimensional spaces.
8
votes
Accepted
Minimizing the perimeter around an obstacle
For any sensible definition of perimeter, an adaptation of following argument proves the claim. Consider the nearest-point projection map $p_A:\mathbb R^n\to A$ (that is, for every $x\in\mathbb R^n$, …
- 32.4k
19
votes
Accepted
Minimal surface which divides a convex body into two regions of equal volume
The conjecture as you state it is false. The variational argument (that can be interpreted in terms of fluid pressure if you like) shows that the surface has constant mean curvature and is orthogonal …
- 32.4k