bio | website | sites.google.com/site/… |
---|---|---|
location | Haifa, Israel | |
age | ||
visits | member for | 1 year, 5 months |
seen | Apr 2 at 20:58 | |
stats | profile views | 552 |
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. |