论文标题
在涉及二维范围内具有对数权重的临界强度和Sobolev型不平等的特征值问题上
On eigenvalue problems involving the critical Hardy potential and Sobolev type inequalities with logarithmic weights in two dimensions
论文作者
论文摘要
我们考虑了涉及关键强力潜力的Neumann边界条件的Laplacian的二维特征值问题。我们证明了第二征函数的存在，并研究了其围绕起源的渐近行为。一个关键工具是具有对数权重的Sobolev类型不等式，本文显示为加权非线性潜在理论的应用。
We consider the two-dimensional eigenvalue problem for the Laplacian with the Neumann boundary condition involving the critical Hardy potential. We prove the existence of the second eigenfunction and study its asymptotic behavior around the origin. A key tool is the Sobolev type inequality with a logarithmic weight, which is shown in this paper as an application of the weighted nonlinear potential theory.
