Conferenciante: David Ruiz (Universidad de Granada)
Título: "Some results on overdetermined elliptic problems"
Fecha y hora: Martes 7 de febrero de 2017, 13:10
Lugar de encuentro: Seminario de la primera planta, IEMath-GR
In this talk we consider an elliptic semilinear problem under overdetermined boundary conditions: the solution vanishes at the boundary and the normal derivative is constant. These problems appear in many contexts, particularly in the study of free boundaries and obstacle problems. Here the task is to understand for which domains (called extremal domains) we may have a solution. This question has shown a certain parallelism with the theory of constant mean curvature surfaces, and also with the well-known De Giorgi conjecture.
The case of bounded extremal domains was completely solved by J. Serrin in 1971, and the ball is the unique such domain. Instead, the case of unbounded domains is far from being completely understood. In this talk we give a rigidity result in dimension 2, and also a construction of a nontrivial extremal domain.