free boundary problems

Katerina Nik

Professor Nik studies partial differential equations that describe phenomena in biological growth processes, fluid dynamics, and mechanical engineering.

A brief introduction to the obstacle problem regularity theory

Prof. Eduardo Teixeira, Department of Mathematics, University of Central Florida (USA)

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B1 L4 R4102

Abstract How does an elastic membrane lie on a given obstacle? This naive looking question hides a beautiful mathematical theory integrating powerful tools with far-reaching applications. In this mini-course we will discuss the obstacle problem as a free boundary model. All necessary tools will be carefully constructed from scratch. We will mainly focus on: optimal regularity of solutions, non-degeneracy estimates, weak geometric-measure properties of the free boundary, classification of global profiles, and differentiability of the free boundary. Brief Biography Eduardo Teixeira is a Full

Rafayel Teymurazyan

Rafayel Teymurazyan works on nonlinear partial differential equations and free boundary problems arising from applications in bio-technologies, chemical engineering, financial mathematics, and optimal design, among others.

Miguel Urbano

Professor Urbano’s research interests are in regularity theory for nonlinear partial differential equations, in particular of singular or degenerate type, arising from different applications, like phase transitions, flows in porous media or semi-supervised learning. He is also interested in free boundary problems, focusing on understanding the local behaviour of weak solutions and the geometric properties of interfaces.