An Elliptic-Parabolic Free Boundary Problem with Discontinuous Data

Explore an advanced mathematical lecture examining elliptic-parabolic free boundary problems characterized by discontinuous data, presented by María Soria-Carro as part of the Erwin Schrödinger International Institute's comprehensive thematic programme on Free Boundary Problems. Delve into the theoretical foundations and analytical techniques required to handle the complexities that arise when dealing with discontinuous boundary conditions in mixed-type partial differential equations. Investigate the mathematical challenges posed by the transition between elliptic and parabolic regimes while managing data discontinuities that significantly impact solution behavior and regularity properties. Examine specialized methods for proving existence, uniqueness, and regularity results in this sophisticated area of mathematical analysis. Gain insights into current research developments in free boundary theory and understand how discontinuous data affects the classical approaches to solving these fundamental problems in mathematical physics and applied mathematics.