论文标题
$ \ mathbb {r}^n $上约束的半线性椭圆系统
Constrained Semilinear Elliptic Systems on $\mathbb{R}^N$
论文作者
论文摘要
我们证明了$ h^1中的解决方案$ u $的存在（\ Mathbb {r}^n，\ Mathbb {r}^m）$在以下非常耦合的半椭圆形PDES上的半连接系统上的$ \ \ \ m i \ mathbb {R} x \ in \ mathbb {r}^n，\] thentwise约束。我们介绍了合适的面化度的构建，这使我们能够在有限的域上解决上述系统。证明的关键步骤包括表明，通过使用所谓的尾部估计值，截断系统的解决方案的顺序在$ H^1 $中是紧凑的。
We prove the existence of solutions $u$ in $H^1(\mathbb{R}^N,\mathbb{R}^M)$ of the following strongly coupled semilinear system of second order elliptic PDEs on $\mathbb{R}^N$ \[ \mathcal{P}[u] = f(x,u,\nabla u), \quad x\in \mathbb{R}^N, \] whith pointwise constraints. We present the construction of the suitable topoligical degree which allows us to solve the above system on bounded domains. The key step in the proof consists of showing that the sequence of solutions of the truncated system is compact in $H^1$ by the use of the so-called tail estimates.
