# Tagged Questions

Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.

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### Estimating sums with restrictions to different Frequencies

I have problems understanding two (for my research important) details in the Proof of Theorem 4 (page 14) in this paper: http://arxiv.org/abs/1209.1518. Notation is very straightforward and is found ...
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### A long-lasting conjecture of Pólya & Szegő

There is a conjecture by Pólya & Szegő (~1950) which is as follows: "Of all $n$-gons of a fixed area, the regular $n$-gon minimizes the first Dirichlet eigenvalue." Surprisingly, this is still ...
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### Well-definedness on $C_{0}^{\infty}(\mathbb{R}^{n})$

Let $T$ be a Calderon-Zygmund operator associated to a Calderon-Zygmund kernel $K\in CZK_{\alpha}$ of order $\alpha>0$ and $b\in BMO(\mathbb{R}^{n})$. Then for $f\in C_{0}^{\infty}(\mathbb{R}^{n})$ ...
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### Explicit solution for one-dimensional Gelfand problem

I wonder if the ODE $y''+e^{y}=a$ can be solved explicitly. For $a=0$, it is well-known that there is a two-parameter family of explicit solutions $y=\ln(2)-2\ln(\cosh(cx+d))+2\ln(c)$, $c,d \in R$...
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### Prescribed curvature problem of a connection beyond the real analytic category for $SL(3,R)$ bundles?

With reference to the questions Does the Riemann-Christoffel curvature determine the connection? and When is a given matrix of two forms a curvature form?, and recalling the following important result ...
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### Estimates for Klein-Gordon-Equation follow directly from Wave equation Estimates

in this paper http://arxiv.org/pdf/1412.1626.pdf it says that Lemma 3.1/(3.1) follows from Theorem 1.3 in http://arxiv.org/pdf/math/0402192.pdf without extra details. Can somebody please explain that? ...
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### $L^p$-bounding inequality [closed]
Do we have that$$\|Du\|_{L^{2p}} \le C\|u\|_{L^\infty}^{1\over2} \|D^2u\|_{L^p}^{1\over2}$$for $1 \le p < \infty$ and all $u \in C_c^\infty(U)$? Here, $U$ denotes an open subset of $\mathbb{R}^n$.