regularity theory

The invisible architect

4 min read · Sun, Feb 8 2026

Spotlight News Research in Focus

free boundary problems nonlinear PDEs regularity theory

Most people never see the mathematics running beneath modern life. CEMSE Professor Miguel Urbano is making sure it works when it matters most.

Miguel Urbano

Professor, Applied Mathematics and Computational Science

nonlinear PDEs free boundary problems regularity theory

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.