597 reputation
211
bio website sites.google.com/site/…
location Haifa, Israel
age
visits member for 1 year, 5 months
seen Apr 2 at 20:58
Post-Doctoral Researcher at the Technion. Interested in PDE, Calc. of Var., Sobolev Space, GMT, and now Harmonic Analysis.

Nov
15
comment Alternative representations of Sobolev space
Aha! I have regained my account! So the answer is yes, and I can send you a preprint if you are interested to the development. I perfectly well understand what you are saying, and the notion is quite interesting.
Nov
14
awarded  Yearling
Jun
25
awarded  Revival
Jun
25
awarded  Promoter
May
28
answered Is BV2 space closed in L2 space?
Apr
25
comment variational characterization of the average of an $L^p$ function
Try taking the derivative of $f(c):=\int_\Omega |u-c|^p\;d\mu$, and then think about justifying it later (dominated convergence, etc). Then you can see why $c$ should be the average of $u$ when $p=2$, and what you might expect otherwise.
Apr
25
accepted Optimality of p-Lebesgue Differentiation Theorem for Sobolev Functions
Apr
24
comment A suitable Sobolev-type space
In general, the $L^\infty$ norm can be controlled by the Sobolev norm within the right parameters, but the converse cannot be true. Sobolev functions have some nice properties of the derivatives, but $L^\infty$ (even continuous, H$\"o$lder continuous) can have pathologically bad derivatives.
Apr
22
revised Optimality of p-Lebesgue Differentiation Theorem for Sobolev Functions
deleted 562 characters in body; edited title
Apr
21
revised Optimality of p-Lebesgue Differentiation Theorem for Sobolev Functions
deleted 13 characters in body
Apr
19
revised Optimality of p-Lebesgue Differentiation Theorem for Sobolev Functions
too many functions named f
Apr
19
asked Optimality of p-Lebesgue Differentiation Theorem for Sobolev Functions
Apr
17
accepted Finding a good ordering of $\mathbb{Q}$
Apr
17
comment Finding a good ordering of $\mathbb{Q}$
Thanks for the reference Sean. What I want to prove is false! Great to know now :)
Apr
17
asked Finding a good ordering of $\mathbb{Q}$
Apr
14
awarded  Organizer
Apr
1
comment A question on optimal Sobolev inequality.
Symmetrization and ODE analysis.
Mar
17
answered Interior regularity for elliptic equations
Mar
16
comment Interior regularity for elliptic equations
Ok. Sorry for the delay. I read what you wrtoe more closely and apologize for missing the $0 \in \partial \Omega$. However, the question you mention is not unique, since in general, the solution $u=0$ is a regular solution. So maybe the question is not correct in asserting solvability in the right space versus the operator is bounded from one space to the other (and in fact, as you show, could be bounded on some functions not in this space).
Mar
13
comment Interior regularity for elliptic equations
I guess I am saying that we do not have $\Delta u =0$ or $\Delta u_m=0$. In fact, we have $\Delta u = \delta_0$ and $\Delta u_m = \delta_{x_m}$, so the equation satisfied by $u,u_m$ is with a right hand side in $(C_0(\Omega))^\prime$, and therefore the standard estimates can not be used, and something else is needed.