Skip to main content
Search type Search syntax
Tags [tag]
Exact "words here"
Author user:1234
user:me (yours)
Score score:3 (3+)
score:0 (none)
Answers answers:3 (3+)
answers:0 (none)
isaccepted:yes
hasaccepted:no
inquestion:1234
Views views:250
Code code:"if (foo != bar)"
Sections title:apples
body:"apples oranges"
URL url:"*.example.com"
Saves in:saves
Status closed:yes
duplicate:no
migrated:no
wiki:no
Types is:question
is:answer
Exclude -[tag]
-apples
For more details on advanced search visit our help page
Results tagged with
Search options questions only not deleted user 44981

Questions on the calculus of variations, which deals with the optimization of functionals mostly defined on infinite dimensional spaces.

15 votes
1 answer
1k views

Who first resolved Hilbert's 20th problem?

Hilbert's 20th problem concerns the existence of solutions to the fundamental problem in the calculus of variations. I understand that Hilbert, Lebesgue and Tonelli were pioneers in this area. In pa …
Nirav's user avatar
  • 347
5 votes
0 answers
101 views

Minimisers and critical points of variational integrals

In the following we consider $\Omega\subset\mathbb{R}^n\ (n\geq2)$ to be open, bounded and with Lipschitz boundary. Consider the following regular variational integral: \begin{equation*} I[u]=\int_{\O …
Nirav's user avatar
  • 347
2 votes
0 answers
64 views

A counterexample to regular boundary points for minimizers of variational integrals under su...

Let $\Omega\subset\mathbb{R}^n$ for some $n\geq 3$ be an open bounded set with at least Lipschitz boundary. Let $p\in (1, 2), N>1$ and $f: \overline{\Omega} \times\mathbb{R}^N\times\mathbb{R}^{Nn}\rig …
Nirav's user avatar
  • 347
1 vote
0 answers
554 views

Reverse Holder Inequality and the higher integrability of the gradient of a solution to Eule...

In Giaquinta-Giusti's (1978) paper "Nonlinear Elliptic Systems with Elliptic Growth" (thm 1.1) they consider the following system: \begin{equation} \sum_{i, j=1}^{n}\sum_{\alpha, \beta=1}^N\frac{\par …
Nirav's user avatar
  • 347