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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 :-) |