3
votes
1answer
141 views

Erroneous calculus of variations reference in V. I. Arnold's Mathematical Methods of Classical Mechanics?

The beginning of section 12, Calculus of variations (chapter 3, Variational principles) in V. I. Arnold's Mathematical Methods of Classical Mechanics (2nd edition, p. 55) reads: For what follows, ...
3
votes
0answers
44 views

Regularity of a Weak Solution

Suppose that $\rho \in L^1(\mathbb{R}^n \times (0,T))$ for every $T < \infty$ is a weak solution of the PDE \begin{align} \partial_t\rho &= \Delta \rho + \text{div}(\rho\nabla\Psi(x))\\ \rho(t ...
0
votes
1answer
15 views

about lower semicontinuous functional

Let $X$ a topological space.My book define : A functional $\varphi: X \rightarrow R$ is lower-semicontinuous (l.s.c) if $\varphi^{-1}(a, + \infty)$ is open in $X$ for any $a \in R.$ (1) And the book ...
6
votes
0answers
99 views

References on the Nash-Moser Implicit Function Theorem

To learn, the Nash-Moser implicit function theorem, I tried with Hamilton (1982) The Inverse Function Theorem of Nash and Moser. But, the article is very encyclopedic. I have a background in ...
2
votes
1answer
76 views

Inverse problem in calculus of variations

I am interested in knowing which differential equations follow from a variational principle. I am reading this and it provides the answer for ordinary differential equations. Is there a complete ...
2
votes
1answer
76 views

Formal Variational Calculus Reference Request

I want to ask for a reference to study Variational Calculus from a formal point of view. What I mean is that many of the references that I've found are inside Physics books, and the authors do not ...
1
vote
0answers
180 views

Problem of finding strong maxima or minima of a functional

I have got this problem in exam where I have to to check for strong maxima (or minima) or weak maxima(or minima) of the functional given by $\int_{0}^{1} (1+x)(y^')^2 dx ~~~~~ y(0) = 0, ~~ y(1) = ...
4
votes
1answer
240 views

Online tutorial requested: functional derivatives

I am taking a course on Quantum Field Theory where we work alot with the functional derivative. Does anyone know of a good, free online PDF tutorial with some examples? Cheers!
1
vote
0answers
268 views

Book Recommendation Needed: Gradient Descent, Euler-Lagrange

On a lecture note I read about Calculus of Variations faculty.uml.edu/cbyrne/cov.pdf the author talks about Euler-Lagrange equation, then continues to say "unfortunately, many times a closed form ...
0
votes
2answers
494 views

Reference request: Calculus of Variations “cheat sheet”

I would appreciate any suggestions for "cheat sheets" (summary sheets) on the calculus of variations/ variational calculus in particular on the Euler -Lagrange equation, Lagrange multipliers, Legendre ...
7
votes
5answers
2k views

Introductory text for calculus of variations

I am currently working on problems that require familiarity with calculus of variations. I am fairly new to this field. Please suggest a good introductory book for the same that could help me pick up ...