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age 28
visits member for 1 year, 11 months
seen Mar 20 at 22:01

Mar
18
comment Schauder estimate on a bounded domain
Mmm, I don't see how that can be true. Take $u$ the solution to $$ \Delta u=0 \text{ in }U $$ and $$ u=g(x,y) \text{ on }\partial U $$. Here $g$ is a smooth function. Then the right hand side vanishes, but the function $u$ is not necessarily constant.
Oct
13
accepted Relationship between LlogL and Hardy spaces
Oct
13
revised Relationship between LlogL and Hardy spaces
edited tags
Oct
13
asked Relationship between LlogL and Hardy spaces
Sep
1
comment Interpolation between L^1 and Sobolev Space
It is a very interesting question. Maybe a good start point is Lemma 5.3 in arxiv.org/pdf/1104.0306.pdf and Lemma 6.6 in arxiv.org/pdf/0812.4979v1.pdf I would also suggest to think on homogeneous Sobolev spaces, the embeding operator and the Riesz-Thorin Theorem.
Jun
5
accepted A bound in Sobolev spaces of negative order
Jun
3
revised A bound in Sobolev spaces of negative order
edited title
Jun
3
asked A bound in Sobolev spaces of negative order
Apr
15
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