本项目中，我们首先拟研究拉普拉斯和分数阶拉普拉斯混合型算子的基本解和Green函数，然后利用基本解以及Green函数的渐近性态处理相应的带Radon测度的椭圆型问题，关于这类问题，我们拟研究其弱解的存在性、唯一性和正则性，以及测度为Dirac测度时弱解的渐近性。这种混合型算子是介于分数阶拉普拉斯与拉普拉斯之间的一种非局部算子，因此，对其椭圆问题的研究有利于我们进一步揭示非局部椭圆问题与二阶椭圆问题之间的共性和区别。

In this program, we first study the fundamental solution and the Green's function for the operator mixed by laplacian and fractional laplacian. Then we make use of its fundamental solution and Green's function to do corresponding elliptic problems involving Radon measures. We will consider the existence, uniqueness and regularity of weak solutions to the above problems. Moreover, the asymptotic behavior of weak solutions are charactered when the measure is Dirac mass. This operator is a nonlocal operator between the fractional laplacian and the laplacian. By studying our nonlocal elliptic problems, we want to make a good understanding about the commonness and difference between the nonlocal elliptic problems and the second order elliptic problems.