Special Session 37: Global or/and blowup solutions for nonlinear evolution equations and their applications
Contents
We discuss the existence of smooth solutions to a class of strongly coupled elliptic systems consisting of two or more equations. Since maximum principles for such systems are not available, the solutions are not known to be bounded a priori and the ellipticity constants can be unbounded. The theories of BMO functions and $A_p$ weights are used here to bypass these obstacles to provide the existence of classical solutions to the systems.