Wednesday 11 November 2026 at 4:45 pm, as part of the Insalate di Matematica seminar cycle, Paolo Malanchini (University of Milano-Bicocca) will hold the following talk
Title: When Ellipticity Fails: Variational Problems Driven by the Grushin Operator
Abstract: The Laplace operator is the standard uniformly elliptic operator. In this classical framework, we can easily recover smooth solutions and establish positivity via the strong maximum principle. But what happens when ellipticity fails? In this talk, we explore nonlinear problems driven by a degenerate elliptic operator: the Grushin operator. We first employ variational tools-such as the Mountain Pass Theorem-to establish existence results for different Grushin problems. Then, we tackle the most delicate part: regularity theory. Unlike the uniformly elliptic case, we cannot expect smooth solutions. However, by using De Giorgi/Moser iteration schemes and Harnack inequalities, we can still recover global boundedness and Hölder continuity of the solutions.
Keywords: Grushin operator, variational methods, regularity theory
Information to attend
The seminar will be held in Room U9-05 (U9 Building | Viale dell’Innovazione 10, Milano) and will also be available online by this link.
For more information, visit the website