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Results tagged with calculus-of-variations
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user 113756
Questions on the calculus of variations, which deals with the optimization of functionals mostly defined on infinite dimensional spaces.
3
votes
Accepted
Difference between variation and differential
I'll try to answer to your questions in their order of appearance below.
How is the variation $\delta y$ different from the differential $dy$? one of the books i tried to use to understand this says …
- 6,367
4
votes
Accepted
Functional derivatives on Banach spaces
Premise: almost (if not) all derivations below are kept at a formal level, i.e. (apart from the notes, almost) no discussion of the hypotheses needed to make the result rigorous are given. This is bec …
- 6,367
6
votes
Almgren's mimeographed lectures notes on varifolds
This question has already an accepted answer and it was long inactive: nevertheless I find compelling to say what I just found by googling the internet. It seems that recently the IAS has started a Di …
- 6,367
7
votes
Representing a nonlinear elliptic PDE as an energy minimization problem
As already said by Kosh, you are trying to solve an inverse problem in the calculus of variation: in its classical formulation, given a system of PDE, the problem consists in finding a functional whos …
- 6,367
8
votes
Accepted
What happens if we consider functions of bounded variation that are not in $L^1$?
The main historical reason for which the requirement $f\in L^1$ enters in the definition of $BV$ is that functions of bounded variation (tout court) of several variables were introduced by Lamberto Ce …
- 6,367
1
vote
Accepted
Fréchet derivative of evaluation-like functional (multivariate)
The general procedure for the identification of a Fréchet derivative is the following
Calculate the functional derivative of the given functional, then
verify its linearity and
verify its continuity …
- 6,367