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Results tagged with ca.classical-analysis-and-odes
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user 479534
Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
3
votes
1
answer
211
views
The energy of a semilinear ODE
I'm currently reading Caffarelli, Gidas, Spruck's paper "Asymptotic Symmetry and Local Behavior of Semilinear Elliptic Equations with Critical Sobolev Growth". For some background, we consider a non-n …
- 457
2
votes
0
answers
200
views
Failure of Calderón–Zygmund inequality at the endpoints
$\newcommand\norm[1]{\lVert#1\rVert}\newcommand\abs[1]{\lvert#1\rvert}$I'd like to prove that the famous Calderón–Zygmund elliptic estimate $$ \norm{ \partial_{ij}u }_{L^p} \leq C \norm{\Delta u }_{L^ …
- 457
2
votes
Accepted
Reference needed: estimate of the second order derivatives
For your estimate to hold on a bounded domain we clearly need $u$ to have zero boundary value, otherwise we can just take a (nonlinear) harmonic function to see that it cannot be true. So assume $u \i …
- 457
6
votes
1
answer
414
views
Lipschitz property of the symmetric rearrangement
I'm currently reading Talenti's paper "Best constant in Sobolev inequality" and am rather stuck on an argument on pg 363 (or pg 11 if you're reading the pdf). In this section of the paper, Talenti is …
- 457