Location: Zoom
https://unm.zoom.us/j/96832154356?pwd=S3BpaDd1TkNCQmN2L3lZdmVDUXdzUT09
Meeting ID: 968 3215 4356
Passcode: 31415926

 

Title: Regularity of free interfaces in parabolic transmission problems arising from the jump of conductivity

 

Abstract: Free boundary problems describe natural phenomena that arise in diverse fields such as physics, biology, and engineering. The analysis of free boundaries has been a central topic in PDEs over the past fifty years, and it is still a very active research topic with numerous open problems. In this talk, we will introduce a two-phase parabolic free boundary problem motivated by the jump of conductivity in composite materials that undergo a phase transition. Our main goal will be to establish strong regularity properties of the free boundary, following the classical strategy: I. Flat free boundaries are C^{1,\alpha}; II. C^{1, \alpha} implies smooth. In the first part, we will focus on the main ideas and techniques developed by Daniela De Silva for elliptic Bernoulli problems, and we will discuss how to adapt these methods to our parabolic context. In the second part, we will introduce the Hodograph transform as a tool to achieve higher regularity of the free boundary. This is a joint work with Dennis Kriventsov.

 

Bio: Maria Soria Carro is a Hill Assistant Professor at Rutgers University, working with Dennis Kriventsov and Yanyan Li. Her research field is Partial Differential Equations. She obtained her Ph.D. in Mathematics at The University of Texas at Austin under the direction of Luis Caffarelli and the co-direction of Pablo Raúl Stinga. She was awarded the AWM Dissertation Prize by the Association for Women in Mathematics, and the Premios Vicent Caselles by the Real Sociedad Matemática Española and Fundación BBVA.