Some methods in non-linear analysis

Congming Li, University of Colorado, Boulder

I will show you two basic methods in nonlinear analysis which will be used in my talk but are too basic to elaborate there. The first one is the so called the 'regularity lifting': You got solutions for your PDE in certain natural spaces and yet we know the solutions should be better in many cases! Here is a method to get better regularities. Next is the method for showing global existence which is based on a simple ODE theory.