当源项为L^1时p-Laplace方程有界弱解的存在性

Existence of bounded weak solutions to a p-Laplace equation with source term in L^1

研究一个p-Laplace方程弱解存在性问题,方程主要的特征是源项f仅仅位于L^1中。借助于方程低阶项系数与右端源项的正则化效应,证明了弱解的先验L~∞估计。利用一致L~∞界,最终得到了弱解的存在性。

The existence of solutions to a p-Laplace equation is studied.The source term f only lies in L1,which is the main feature of the problem.With the help of the regularizing effect between the coefficient of the lower order term and the source term,a priori L∞regularity for its weak solutions is proved.B y the uniform L∞bound,the existence of weak solutions is obtained.