网络风铃

摘要： Here we collect some results from "Classification of solutions for an integral equation}, {\it Comm. Pure Appl. Math." toexplain 1--5 in last noteA. For $N$ a integer and $0<\alpha<N/2$, the integral equation \begin{equation}\label{eq:int} u(x) = \int_{\mathbb R^N} \frac1{|x-y|^{N-2\ 阅读全文

摘要： Consider the fractional elliptic equation\begin{equation}\label{3.3}(-\Delta)^{\alpha} W-|W|^{\frac{4\alpha}{N-2\alpha}}W = 0.\end{equation}It was known that \[W(x) = C \left(\frac{1}{1+|x|^2}\right)^{\frac{N-2\alpha}2}\] is in $\dot{H}^{\alpha/2}(\mathbb{R}^N)$ and solves the fractional elliptic eq 阅读全文

摘要： <script type="text/x-mathjax-config">MathJax.Hub.Config({tex2jax: { inlineMath: [['$','$'], ['\\(','\\)']], processEscapes: true },TeX: { equationNumbers: { autoNumber: ["AMS"], useLabelIds: true } }, "HTML-CSS": { linebreaks: { aut 阅读全文

摘要： 可以看出\[\sum_{\xi\in D_i} a(\xi) e^{ix\cdot\xi} = c'M^{n-1} \sum_{\xi\in D_i} \int_{S_{\xi}} g_i(\zeta)e^{ix\cdot\xi}\sigma(d\zeta)\]进一步\[ c'M^{n-1} \sum_{\xi\in D_i} \int_{S_{\xi}} g_i(\zeta)e^{ix\cdot\xi}\sigma(d\zeta) = c'M^{n-1} \int_{S} \Big[\sum_{\xi\in D_i} \chi_{S_{\xi}} e^{ix\cdot 阅读全文

摘要： 考虑如下振荡积分：\[Tf(x) = \int e^{i\phi(x,y)} f (y) dy \qquad (|f|\le 1).\] 其中$y\in \Omega$是一个包含原点的邻域，$x\in\{x\in\mathbb{R}^3||x|<R\}$. 阅读全文