论文标题
关于具有恒定系数的二阶椭圆系统的能量功能
On energy functionals for second-order elliptic systems with constant coefficients
论文作者
论文摘要
我们考虑具有恒定系数的二阶椭圆系统的差异问题。我们证明，这种类型的不可还原的椭圆形系统不承认表格$ f \ mapsto \ int_ {d} \ varphi（u_x，v_x，v_x，u_y，u_y，v_y，v_y）\，dxdy $ d $ d $ d p y in IS $ five的n y y y y y y y p \ d varphi，我们在$ warph y in p \ $ \ mathbb r^4 $，$ f = u+iv $是复杂变量中的一个函数。该证明是基于将所考虑的系统减少为特殊（规范）形式的，当定义该系统的差分运算符表示是针对两个小的实际参数（正在考虑的系统的规范参数）表示Laplace运算符的扰动。
We consider the Dirichlet problem for second-order elliptic systems with constant coefficients. We prove that non-reducible strongly elliptic systems of this type do not admits non-negatively defined energy functionals of the form $f\mapsto\int_{D}\varPhi(u_x,v_x,u_y,v_y)\,dxdy$, where $D$ is the domain where the problem we are interested in is considered, $\varPhi$ is some quadratic form in $\mathbb R^4$, and $f=u+iv$ is a function in the complex variable. The proof is based on reducing the system under consideration to a special (canonical) form, when the differential operator defining this system is represented as a perturbation of the Laplace operator with respect to two small real parameters (the canonical parameters of the system under consideration).
