2 papers
math.NA2021
Expected uniform integration approximation under general equal measure partition
Jun Xian, Xiaoda Xu
In this paper, we study bounds of expected discrepancy to give mean square error of uniform integration approximation for functions in Sobolev space $\mathcal{H}^{\mathbf{1}}…
math.AP2021
The existence of solutions for nonlinear elliptic equations: Simple proofs and extensions of a paper by Y. Shi
Xiaodan Xu, Rafael de la Llave, Fenfen Wang
The paper [Shi19] uses the Craig-Wayne-Bourgain method to construct solutions of an elliptic problem involving parameters. The results of [Shi19] include regularity assumptions on…