论文标题
在边界条件下耦合的狄拉克系统上
On Coupled Dirac Systems under Boundary Condition
论文作者
论文摘要
在本文中，我们研究了Dirac Systems \ begin {equation} \ label {e：0.1} \ left \ {\ begin {array} {c}的解决方案的存在。 pu = \ frac {\ partial h} {\ partial v}（x，u，v）\ quad \ hbox {on} \ m， pv = \ frac {\ partial h} {\ partial u}（x，u，v）\ quad \ hbox {on} \ m， b _ {\ text {chi}} u = b _ {\ text {chi}} v = 0 \ quad \ hbox {on} \ \ \ partial m \ end m \ end end {array} \ right。 \ end {equation}其中$ m $是$ m $二维紧凑型的riemannian旋转歧管，带有光滑边界$ \部分m $，$ p $是在边界条件$ b _ {\ text {chi}} {chi}} { c^{\ infty}（m，σm）$是旋转器。使用分数Sobolev空间的适当产物的分析框架，获得了耦合Dirac系统的解决方案结果，以实现超质量生长速率的非线性。
In this article we study the existence of solutions for the Dirac systems \begin{equation}\label{e:0.1} \left\{ \begin{array}{c} Pu=\frac{\partial H}{\partial v}(x,u,v) \quad\hbox{on} \ M, Pv=\frac{\partial H}{\partial u}(x,u,v) \quad\hbox{on} \ M, B_{\text{CHI}}u= B_{\text{CHI}}v=0\quad\hbox{on} \ \partial M \end{array} \right. \end{equation} where $M$ is an $m$-dimensional compact oriented Riemannian spin manifold with smooth boundary $\partial M$, $P$ is the Dirac operator under the boundary condition $B_{\text{CHI}}u= B_{\text{CHI}}v=0$ on $\partial M$, $ u,v\in C^{\infty}(M,ΣM)$ are spinors. Using an analytic framework of proper products of fractional Sobolev spaces, the solutions existence results of the coupled Dirac systems are obtained for nonlinearity with superquadratic growth rates.
