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age 28
visits member for 2 years, 3 months
seen Jul 17 at 8:13

May
17
awarded  Critic
May
8
awarded  Curious
Apr
29
comment Boundedness of heat semigroup on $L^1(\Omega)$
For positive $f$ and neumann BC for the laplacian, you can prove the conservation of the $L^1$ norm by using the divergence theorem.
Apr
14
accepted Mathematical difference between entropy and energy
Apr
14
comment Mathematical difference between entropy and energy
where can I see this computation? Can you give me a reference?
Apr
14
awarded  Nice Question
Apr
13
comment Mathematical difference between entropy and energy
Thank you for your comment. I already knew about the term "free energy". There is another question arising here: what is the difference between and energy and a free energy?
Apr
13
comment Mathematical difference between entropy and energy
Thank you for your answer! Actually, there are examples where $H$ does not decay (for instance, the parabolic-elliptic) Keller-Segel. Also, I would say that the regularity to preserve $L^2$ for the Euler flow and the regularity to preserve $LlogL$ is the same, $C^{1/3}$. Isn't it? With this I meant that there should be something else, not merely the monotonicity or well-behaviour. Am I right?
Apr
13
comment Mathematical difference between entropy and energy
Thank you for your answer! I was assuming $u_0$, to be positive, so there was no problem on difining the entropy. Why do you say the case $2=p$ is the usual energy inequality? Maybe is a stupid question, but, even if I see that this quotient has the same flavour, I don't see why it's the same thing.
Apr
13
asked Mathematical difference between entropy and energy
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 :-)