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Results tagged with calculus-of-variations
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user 90655
Questions on the calculus of variations, which deals with the optimization of functionals mostly defined on infinite dimensional spaces.
3
votes
1
answer
409
views
Question on Harmonic maps between Riemannian manifolds
In Theory of harmonic maps, main goal is to find minimum of Dirichlet energy function which is defined as follows:
$$E(f):=\frac{1}{2}\int_M\|df\|^2dvol_g\qquad f:(M,g)\to(N,h).$$
In many Books such a …
- 4,195
3
votes
1
answer
990
views
Manifold structure of the set of all smooth functions between two smooth manifolds!
In the studies of the calculus of variation, a map $f:M\to N$ said to be harmonic if it is a critical point of the Dirichlet energy function. i. e.
\begin{align}
E:C^\infty(M,N)&\longrightarrow \Bbb …
- 4,195