一类P-Laplace型椭圆方程组非常弱解的存在性

Existence of very weak solutions for a class of P-Laplacian elliptic equations

为了建立非齐次项是P-Laplace型算子的椭圆方程组非常弱解的存在性,构造适当的相对截断函数作为检验函数,并通过适当形式的权函数,结合相对覆盖分解和权重、散度-旋度定理等偏微分方程证明技巧,得到了具有P-Laplace型椭圆方程组非常弱解的存在性。

In order to establish the existence of very weak solutions for elliptic equations whose in-homogeneous terms are P-Laplace operators,the appropriate relative truncation function was constructed as the test function in the definition of very weak solution.Then through the appropriate form of weight function,combining the relative covering decomposition with partial differential equation proof techniques such as weight and divergence-curl theorem,the desired results of the very weak solutions existence theory for elliptic systems with P-Laplace operator were obtained.