Norm estimate of Green operator, perturbation of Green function and integrability of superharmonic functions
Norm estimate of Green operator, perturbation of Green function and integrability of superharmonic functions
复制标题
Green算子的范数估计、Green函数的摄动和超调和函数的可积性
DOI：
10.1007/s002080050223
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发表时间：
1998
影响因子：
1.4
通讯作者：
Hiroaki Aikawa
中科院分区：
文献类型：
--
作者：
Hiroaki Aikawa
欧几里德空间中开集上拉普拉斯方程的格林算子的算子范数估计以容量的形式给出。这适用于薛定谔方程的格林函数的扰动。薛定谔方程的格林函数在边界附近具有与拉普拉斯方程相当的衰减的充分条件是根据薛定谔方程势的可积条件给出的。这适用于关于薛定谔方程的平滑域的马丁边界。此外，它还与关于寿命估计和非负超调和函数的可积性的克兰斯顿-麦康奈尔不等式有关。
An operator norm estimate of the Green operator for the Laplace equation on an open set in the Euclidean space is given in terms of capacity. This applies to the perturbation of the Green function for the Schrödinger equation. A sufficient condition for the Green function for the Schrödinger equation to have decay near the boundary comparable to that for the Laplace equation is given in terms of an integrable condition for the potential of the Schrödinger equation. This has an application to the Martin boundary of a smooth domain with respect to the Schrödinger equation. Also, it is related to the Cranston-McConnell inequality about the life time estimate and the integrability of nonnegative superharmonic functions.