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8h
reviewed Approve nt.number-theory tag wiki
1d
comment How does the $L^\infty$ norm of the solution of $-\Delta u + \lambda u =0$, $\partial_\nu u=\alpha$ depend upon $\alpha$ and $\lambda$?
Well, if $u\in H^2$, and the dimension is 3 or less, then $u\in L^\infty$ by Sobolev imbedding. So it seems like you answered your own question.
2d
answered If $u \in L^2(0,T;X_0)$ with $u_t \in L^2(0,T;X_2)$, then is $u \in L^\infty(0,T;X_1)$?
Feb
9
comment Continuous inclusions in Hilbert-Sobolev space $H^s(\mathbb{R}^n) \hookrightarrow \mathcal{E}^k(\mathbb{R}^n)$
This is a well-known theorem, proved in many textbooks. Why do you "have to" prove this?
Feb
7
reviewed Approve cryptography tag wiki excerpt
Feb
5
reviewed Approve approximation-algorithms tag wiki excerpt
Feb
5
reviewed Approve ordinal-numbers tag wiki excerpt
Feb
4
reviewed Approve graph-colorings tag wiki excerpt
Feb
2
comment Weak convergence in $L^2(0,T;X)$
As stated, this is not even true for X=R.
Feb
1
revised Can Gradient be controlled by Curl and Divergence in Morrey spaces
corrected spelling
Jan
28
comment Continuity + $H^1$ + Laplacian control $ \implies$ local Lipschitz property
You do not know that $\Delta u\in L^2$. $\Delta u$ might include a surface delta function if $\nabla u$ is discontinuous across $\Sigma$.
Jan
24
comment Resolvent of the operator
So what is the point of the Fourier transform? You are just getting the same operator back.
Jan
24
reviewed Approve finite-geometry tag wiki excerpt
Jan
24
reviewed Approve incidence-geometry tag wiki excerpt
Jan
24
comment Resolvent of the operator
How does $\sqrt{x^2+y^2}$ become $-\partial_\zeta^2-\partial_\eta^2$? Is there a typo here?
Jan
11
comment ODE estimate for boundary value problem
It seems that an answer to this problem requires, in particular, knowledge of all eigenvalues of Sturm-Liouville problems. Life would be nice if that were simple, but ... What kind of answer do you expect?
Jan
11
comment Backgrounds of the p-Laplacian Operator
As you have observed, each term in the equation by itself has a physical motivation, but the combination is not so easily motivated. The true motivation is probably that this combination happens to be something for which the authors succeeded in getting estimates. It is the motivation behind many papers.
Jan
11
answered Selection problem in a collection of non-empty sets
Jan
8
reviewed Approve coq tag wiki
Jan
8
reviewed Approve Diameter vs Radius in Maximal Planar Graphs