User Lorenzo Pompili

6 votes

1 answer

290 views

Analytic maps on Banach spaces: analyticity upgrade

asked Apr 3 at 14:06

5 votes

0 answers

414 views

All $L^pL^q$ estimates for the heat equation on $\mathbb R$ (with gain of derivatives)

asked Mar 21, 2023 at 15:39

5 votes

0 answers

231 views

Non-uniqueness of solutions to a simple nonlinear elliptic PDE in $\mathbb R^n$

asked Sep 28, 2023 at 14:37

5 votes

1 answer

538 views

If $f$ is bounded, decays fast enough at infinity and $\int f=0$, does this imply that $f$ is in the Hardy space $\mathcal H^1(\mathbb R^n)$?

asked Oct 2, 2023 at 17:29

4 votes

0 answers

139 views

Given $a>0$, find $b>0$ for which $\|\langle x\rangle^{-b}|\partial_x|^{1/2}f\|_{L^2}\lesssim\|\partial_x f\|_{L^2}+\|\langle x\rangle^{-a}f\|_{L^2}$

asked Dec 11, 2022 at 14:48

3 votes

0 answers

172 views

Radial-energy decomposition of a velocity field in 2D: is anyone able to show that the lemma below is true (…or false)?

asked Nov 13, 2021 at 0:42

3 votes

1 answer

158 views

Sharp upper bound of the number of edges for graphs of thickness two

asked Oct 1, 2023 at 14:37

1 vote

0 answers

114 views

Global existence for large data in $H^{-1/2}(\mathbb R)$ of viscous Burgers' equation with external forcing

asked Jan 3 at 1:45

1 vote

0 answers

102 views

Burgers' equation with viscosity: modulational analysis and energy estimates for large data

asked Sep 27, 2023 at 16:36

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9 Questions

Analytic maps on Banach spaces: analyticity upgrade

All $L^pL^q$ estimates for the heat equation on $\mathbb R$ (with gain of derivatives)

Non-uniqueness of solutions to a simple nonlinear elliptic PDE in $\mathbb R^n$

If $f$ is bounded, decays fast enough at infinity and $\int f=0$, does this imply that $f$ is in the Hardy space $\mathcal H^1(\mathbb R^n)$?

Given $a>0$, find $b>0$ for which $\|\langle x\rangle^{-b}|\partial_x|^{1/2}f\|_{L^2}\lesssim\|\partial_x f\|_{L^2}+\|\langle x\rangle^{-a}f\|_{L^2}$

Radial-energy decomposition of a velocity field in 2D: is anyone able to show that the lemma below is true (…or false)?

Sharp upper bound of the number of edges for graphs of thickness two

Global existence for large data in $H^{-1/2}(\mathbb R)$ of viscous Burgers' equation with external forcing

Burgers' equation with viscosity: modulational analysis and energy estimates for large data