# Tagged Questions

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, ...
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 ...
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 ...
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 ...
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 ...
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 ...
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) = ...
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!
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 ...
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 ...
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 ...