一类退化型非线性椭圆方程有界弱解的存在唯一性

Existence and Uniqueness of Bounded Weak Solutions for a Class of Degenerate Nonlinear Elliptic Equations

针对一类带有低正则值的退化型非线性椭圆方程,通过选取适当的试验函数,结合主部算子的单调性性质证明了有界解的唯一性;在解的存在性方面,首先针对外立项为本性有界函数的情形,给出有界弱解的存在性;进而利用这一结果及适当的光滑逼近和紧性定理给出了原方程有界弱解的存在性。

For a class of degenerate nonlinear elliptic equations with irregular data,by taking proper test functions,we first prove the uniqueness of solutions. Then we use smooth approximations and proper compactness theorems to provide the existence of bounded weak solutions.