Grushin型算子精确Hardy不等式的一个新证明

摘要

通过选取合适的测试函数,利用二次函数取最值的方法,证明了与Grushin型算子相关的退化椭圆算子的精确Hardy不等式,并给出若干引理.推广了现有文献中的结果.%A generalized sharp Hardy inequality to the degenerate elliptic operators with respect to Grushin type operators is proved by ingeniously choosing test functions and calculating the maximum value of a quadratic equation. Some interesting corollaries are also listed.