ONE-DIMENSIONAL THEORY. REGULARITY AND INTERFACES
Juan Luis Vázquez · 2006
Abstract This chapter presents an introduction to some of the main topics relating to the PME, focusing on non-negative solutions. Section 15.1 presents a detailed analysis of the regularity of the pressure, for which Lipschitz continuity is proved both in space and time. Section 15.2 introduces new comparison results. Shifting comparison, intersection comparison and lap number count are quite useful in the study of interfaces. The study of interfaces is begun in Section 15.3. The growth of the interface is estimated and the waiting time analysed. Section 15.4 deals with some of the main issues of the theory.