KAUST-CEMSE-AMCS-Mathematics-and-Applications-Colloquium-Eduardo-Teixeira

Nonlocal Degenerate PDEs: Bridging Free Boundary Problems and Critical-point Models

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Building 1, Level 3, Room 3426

This talk explores a new class of PDEs featuring nonlocal degeneracies. Our framework unifies two classical scenarios — free boundary problems and critical-point degenerate PDEs; both are recast as local extrema models in our formulation.

For models where the PDE is active only above a given threshold, we prove optimal local Hölder continuity and a Krylov–Safonov–type result with universal estimates. In the globally degenerate case, we establish sharp C1,β regularity estimates which sharply interpolate the classical ones known for the local extrema problems. In addition to its intrinsic significance, this new framework also offers fresh insights into the classical models. This is a joint work with D. Araújo, A. Sobral, and M. Urbano.

Presenters

Eduardo Teixeira, Graduate Director & Professor, Department of Mathematics, University of Central Florida

Brief Biography

Eduardo Teixeira holds the position of Full Professor in the Department of Mathematics at the University of Central Florida, USA. His research focuses on free boundary problems and regularity theory for nonlinear partial differential equations. His research interests also encompass issues in higher education.