【开课说明】

   课程日期：2023年4月24/25/27日

   授课时间：15:00 - 18:00

   课时数：3 课时/天，共9课时 

   ZOOMID：820 6413 2631  密码：tmcc202304    

   课程链接：https://us02web.zoom.us/j/82064132631?pwd=QVh0Nm8wc1dxR3JBTm10U08vOENVdz09

   授课老师：Prof. Paolo Secchi,  University of Brescia

   主办单位：国家天元数学中部中心、武汉大学数学与统计学院

   欢迎参加课程交流学习！联系人：杨老师 电话：027-68788932   Email:  tmcc@whu.edu.cn

【内容摘要】

    The aim of the course is to provide an introduction to the Nash-Moser implicit function theorem, as a tool for the resolution of nonlinear differential equations, where the linearized problems admit estimates with a loss of derivatives with respect to the given data.

    We first introduce the local inversion theorem and the standard implicit function theorem, and discuss some examples where these theorems are sufficient. Then we briefly introduce the isometric embedding problem, that is the problem originally solved by J. Nash in 1956, using an iteration technique taken up again by J. Moser in 1961, and subsequently known as the Nash-Moser method. We also discuss a simple boundary value problem for the wave equation that may admit estimates with a loss of derivatives from the data. Finally, we present the Nash-Moser implicit function theorem with a simplified scheme of proof.