Search Results
| 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 ap.analysis-of-pdes
Search options not deleted
user 51695
Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
1
vote
Equivalence of statements about level sets: $u|_{S \times [\tau, \infty)}$ depends only on $...
If I am not missing something then the corrected statements look equivalent to me on the level of sets, no need for smoothness.
Fix $\tau > 0$ and assume that 1. holds. For any $t\geq \tau$ and $y \in …
- 2,504
4
votes
Accepted
Regular Lagrangian flow for "square root example": $\frac{d}{dt} X(t,x) = \sqrt{X(t,x)}$
Your intuition is right. The key is in the paper you cite, in that they consider uniqueness in the class $L^1_{\text{loc}}$, which does not allow for concentrations. If you add to this, that the Lagra …
- 2,504
6
votes
What is Young measure?
Related to Nate River's answer, I personally prefer to think of Young measures as single measures $\nu$ on $U \times \mathbb{R}^m$, which have the condition that their projection on the first componen …
- 2,504
2
votes
Existence of first variation
In general, a first variation is just the collection of all directional derivatives
$\frac{d}{d\epsilon} \mathcal{F}(\rho+\epsilon\chi)|_{\epsilon = 0}$. For fixed $\rho$ one can treat them as a funct …
- 2,504
4
votes
Accepted
Averaging the mass of a Sobolev function $f\in W^{1,p}(\Omega)$ near $\partial\Omega$
In Evans & Gariepy's "Measure theory and fine properties of functions", Sec. 5.3., they construct the trace operator on a bounded Lipschitz domain $\Omega$ for BV-functions (and thus by inclusion for …
- 2,504
3
votes
Accepted
Must a Schauder basis for $W^{1,p}_0(\Omega)$ be oscillatory?
Even the modified question does not hold.
Let $u_n$ be a basis such that $\mathcal{L}^d(\operatorname{spt} u_n) \to 0$, e.g. a wavelet basis and let $\phi \in C_0^\infty(\Omega)$ a function such that …
- 2,504
0
votes
Derivative of Wasserstein distance $W^p_p$ along solutions of the continuity equation (contr...
Without having read the sources in detail, I would notice the following:
In (4) the second measure is time independent. To satisfy (1) this then corresponds to $(\rho^{(2)}_t,v_t^{(2)}) = (\nu,0)$. Bu …
- 2,504
3
votes
Accepted
How to interpret the vector fields $F_p(x,u,Du)$ in a Lagrangian optimization problem
There is the following interpretation coming from physics and continuum mechanics, which is a bit too long for a comment but might be helpful:
If you think of $\mathcal{F}$ as an energy that you want …
- 2,504
5
votes
Accepted
Existence of directional heat equation without uniform ellipticity
As you do not have any sort of coupling in any spatial direction other than $x_1$, what you have here is not actually a time-dependent PDE in $d$-dimensions but a $(d-1)$-parameter family of time-depe …
- 2,504