论文标题
Caffarelli-kohn-nirenberg型不平等现象与加权$ p $ -laplace方程有关
Caffarelli-Kohn-Nirenberg-type inequalities related to weighted $p$-Laplace equations
论文作者
论文摘要
我们使用与Sobolev不平等相关的合适转换来研究某些与加权$ p $ laplace方程相关的Caffarelli-Kohn-Nirenberg-type不平等的尖锐常数和优化器。此外，我们将分类与与径向极端有关的线性化问题进行分类。作为应用程序，我们通过使用光谱估计与紧凑型参数结合了相关不平等的梯度类型的剩余项，该参数至少在径向案例中扩展了Figalli和Zhang（DukeMath。J.2022）的工作。
We use a suitable transform related to Sobolev inequality to investigate the sharp constants and optimizers for some Caffarelli-Kohn-Nirenberg-type inequalities which are related to the weighted $p$-Laplace equations. Moreover, we give the classification to the linearized problem related to the radial extremals. As an application, we investigate the gradient type remainder term of related inequality by using spectral estimate combined with a compactness argument which extends the work of Figalli and Zhang (Duke Math. J. 2022) at least for radial case.
