主讲人简介：羊丹平，华东师范大学教授、博导，中国计算数学学会副理事长。

内容摘要：In this talk, we present a counter example which shows that the Galerkin weak formulation loses coercivity in the context of variable-coefficient conservative fractional elliptic differential equations. Hence, the previous results cannot be extended to variable-coefficient conservative fractional elliptic differential equations. We adopt an alternative approach to prove the existence and uniqueness of the classical solution to the variable-coefficient conservative fractional elliptic differential equation and characterize the solution in terms of the classical solutions to second-order elliptic differential equations. Furthermore, we derive a Petrov-Galerkin weak formulation to the fractional elliptic differential equation. We prove that the bilinear form of the Petrov-Galerkin weak formulation is weakly coercive and so the weak formulation has a unique weak solution and is well posed. Finally, we outline potential application of these results in the development of numerical methods for variable-coefficient conservative fractional elliptic differential equations.

讲座语言：中文