有界域上局部与全局的Radon测度的积分不等式

Some Local and Global Integral Inequalities with Radon Measure on Bounded Domain

选择Laplace-Beltrami算子Δ和Green算子G的复合算子Δ◇G为研究对象,首先证明了有界域的局部圆域上作用于齐次A-调和方程解的复合算子Δ◇G的带Radon测度的积分不等式,然后在此基础上得到有界域上全局的Radon积分不等式.

In this paper we choose the composite operator Δ◇G of the Laplace-Beltrami operator Δ and the Green’s operator G as the research object.We first prove the local integral inequality with Radon measure for the composite operator Δ◇ G applied to the solutions of the homogeneous A-harmonic equation on the local circle domain of the bounded domain.Furthermore,we also establish the global integral inequality on the bounded domain.