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awarded  Yearling
Apr
2
comment Nonlocal (parabolic) PDEs in the Sobolev space setting
You are welcome :-)
Mar
27
answered Nonlocal (parabolic) PDEs in the Sobolev space setting
Mar
6
comment Integrability of the Poisson integral
Is your $f=P_y*g$ for some $g$? Maybe the result is not true for every $p$. Is the result true for $p=2$, i.e., given $g\in H^1(\mathbb{R})$, is $P_y*g\in L^2(\mathbb{R}\times\mathbb{R}^+)$?
Mar
2
revised Integrability of the Poisson integral
edited body
Mar
2
asked Integrability of the Poisson integral
Feb
26
accepted L logL space and compactness
Feb
26
comment L logL space and compactness
Ok, thank you. Can you give me a reference?
Feb
26
asked L logL space and compactness
Jan
19
awarded  Commentator
Jan
19
comment If $f \in H^{\frac 12}$ and $\varphi$ is Lipschitz, is $f\varphi \in H^{\frac 12}$ (on a Lipschitz hypersurface)?
You can get $$ \|fg\|_{H^{1/2}}\leq \|f\|_{C^1}\|g\|_{H^1} $$ by using interpolation of operators. You can see the paper by Gou & Tice, Analysis and pde, vol 6, n.2m 2013.
Jan
17
answered References for well-posedness of weak solutions to Stefan problem
Jan
12
answered Blow-up for the quasilinear heat equation $u_t= u \ u_{x x}$ or the related $w_t= \left(w_x e^w\right)_x$
Dec
28
comment If $f \in H^{\frac 12}$ and $\varphi$ is Lipschitz, is $f\varphi \in H^{\frac 12}$ (on a Lipschitz hypersurface)?
Mmm, in the case $M=\mathbb{T}$ (or $M=\mathbb{R}$), the bound can be obtained using Kato-Ponce and the Sobolev embedding.
Dec
27
answered If $f \in H^{\frac 12}$ and $\varphi$ is Lipschitz, is $f\varphi \in H^{\frac 12}$ (on a Lipschitz hypersurface)?
Dec
19
answered Maximum of the solution of a parabolic PDE
Dec
18
comment A bound for a product in BMO
Thank you for your answer. However, your answer only says that my approach is wrong. It doesn't say anything on the bound, right?
Dec
17
asked A bound for a product in BMO
Oct
7
answered weak solution of viscous Burgers equation with non-homogeneous Dirichlet boundary conditions
Sep
10
answered Blow up of solutions to parabolic PDEs