User Giorgio Metafune

17 votes

Accepted

Acting with a finite number of rotations on a set of positive measure can you fill almost the whole circle?

answered Apr 27, 2020 at 10:29

9 votes

Gradient $L^p$ estimates for heat equation

answered Mar 1, 2020 at 10:44

8 votes

Accepted

Interpolation theory and $C^k$-spaces

answered Oct 28, 2020 at 8:31

8 votes

Accepted

A problem concerning a divergent function on $[0, 1]$

answered Dec 7, 2021 at 19:53

8 votes

Accepted

Eigenvalues and eigenfunctions of the Laplace operator on entire plane

answered Jan 29, 2022 at 10:18

8 votes

Accepted

Unique solutions to the heat equation on $\mathbb{R}^3$

answered Mar 26, 2022 at 19:02

8 votes

Accepted

Is $L^p(X,\ell^p)$, $1<p<\infty$, uniformly convex?

answered Apr 21, 2022 at 18:06

8 votes

Is it possible to obtain the inequality $\|\nabla f\|_{L^{2p}} \leq C (\|f\|_{L^\infty} \|f\|_{W^{2, p}})^{1/2}$ from interpolation/harmonic analysis?

answered Jan 7 at 10:33

7 votes

Accepted

Why is $\frac{1}{|x|^{n-2}}u(\frac{x}{|x|^2})$ harmonic if $u$ is harmonic?

answered Oct 25, 2022 at 18:43

7 votes

Proving an integral identity

answered Feb 11 at 11:27

7 votes

Accepted

Elementary inequality generalizing convexity of a function on a segment

answered Jul 13, 2020 at 17:07

6 votes

Spherical harmonics – pointwise and L1 bounds

answered Nov 30, 2020 at 9:58

6 votes

Accepted

Angle of analyticity of semigroup

answered Jan 4, 2020 at 18:40

6 votes

Accepted

Does this condition on $f$ imply essential boundedness on compacts?

answered Sep 28, 2022 at 16:44

6 votes

Accepted

Is this an $L^p-L^{\infty}$ operator?

answered Oct 4, 2022 at 20:10

5 votes

Accepted

A function is of bounded variation if and only if the errors of its best approximation by trigonometric polynomials satisfy $\sum\frac{e_n}n<\infty$?

answered Sep 23, 2022 at 22:24

5 votes

Do two ways to differentiate Lipschitz functions coincide?

answered Oct 16, 2022 at 13:39

5 votes

Accepted

The behavior of $ \nabla u $ on the boundary for Poisson equations

answered Mar 3, 2022 at 19:59

5 votes

Accepted

Are there $f, g$ such that $\int_{S^{1}} |f'|^{2}+|g'|^{2}d\theta-2\int_{S^{1}}f'g<0,$ where $f'=\frac{\partial f}{\partial \theta}$

answered Jul 31, 2020 at 9:43

5 votes

2D Fourier transform of log function

answered Aug 11, 2020 at 12:46

5 votes

Accepted

How to use comparison principle to prove the following inequality about Laplace equation?

answered Oct 30, 2022 at 15:30

5 votes

Accepted

A fractional weighted Poincaré inequality

answered Nov 19 at 23:33

4 votes

Accepted

Is the Hardy Littlewood “minimal function” comparable to the original function in $L^1$ norm?

answered Aug 21 at 17:59

4 votes

Accepted

Weak convergence in $H^{1}$ implies different convergence in $L^{p}$?

answered Sep 19 at 20:56

4 votes

Accepted

Total sets for $L^p$ for every $1\leq p < \infty$

answered Mar 23 at 12:05

4 votes

Regularity of Newtonian potential along smooth boundary

answered May 13 at 21:32

4 votes

Accepted

Nonnegativity implies $\langle Lf,f\rangle\geq \int f^2-(\int fg)^2$ for $g\geq 0$

answered Apr 24, 2020 at 19:40

4 votes

Different ways to prove $L^p$-estimates for the heat equation

answered Sep 26, 2020 at 8:32

4 votes

Accepted

Optimal constant in Sobolev embedding

answered Oct 23, 2020 at 18:45

4 votes

Accepted

A detail in one step in a theorem from a paper of Brezis and Merle

answered Oct 15, 2022 at 20:46

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103 Answers

Acting with a finite number of rotations on a set of positive measure can you fill almost the whole circle?

Gradient $L^p$ estimates for heat equation

Interpolation theory and $C^k$-spaces

A problem concerning a divergent function on $[0, 1]$

Eigenvalues and eigenfunctions of the Laplace operator on entire plane

Unique solutions to the heat equation on $\mathbb{R}^3$

Is $L^p(X,\ell^p)$, $1<p<\infty$, uniformly convex?

Is it possible to obtain the inequality $\|\nabla f\|_{L^{2p}} \leq C (\|f\|_{L^\infty} \|f\|_{W^{2, p}})^{1/2}$ from interpolation/harmonic analysis?

Why is $\frac{1}{|x|^{n-2}}u(\frac{x}{|x|^2})$ harmonic if $u$ is harmonic?

Proving an integral identity

Elementary inequality generalizing convexity of a function on a segment

Spherical harmonics – pointwise and L1 bounds

Angle of analyticity of semigroup

Does this condition on $f$ imply essential boundedness on compacts?

Is this an $L^p-L^{\infty}$ operator?

A function is of bounded variation if and only if the errors of its best approximation by trigonometric polynomials satisfy $\sum\frac{e_n}n<\infty$?

Do two ways to differentiate Lipschitz functions coincide?

The behavior of $ \nabla u $ on the boundary for Poisson equations

Are there $f, g$ such that $\int_{S^{1}} |f'|^{2}+|g'|^{2}d\theta-2\int_{S^{1}}f'g<0,$ where $f'=\frac{\partial f}{\partial \theta}$

2D Fourier transform of log function

How to use comparison principle to prove the following inequality about Laplace equation?

A fractional weighted Poincaré inequality

Is the Hardy Littlewood “minimal function” comparable to the original function in $L^1$ norm?

Weak convergence in $H^{1}$ implies different convergence in $L^{p}$?

Total sets for $L^p$ for every $1\leq p < \infty$

Regularity of Newtonian potential along smooth boundary

Nonnegativity implies $\langle Lf,f\rangle\geq \int f^2-(\int fg)^2$ for $g\geq 0$

Different ways to prove $L^p$-estimates for the heat equation

Optimal constant in Sobolev embedding

A detail in one step in a theorem from a paper of Brezis and Merle