Events

This talk concerns fully nonlinear stationary logistic-type equations of the form F(x,D^2u) + μu = k(x)u^p, with p > 1 and k(x) ≥ 0, in a bounded domain with Dirichlet boundary condition. We study the existence, uniqueness, and nonexistence of positive solutions depending on μ, and we analyze the asymptotic behavior of solutions as μ…

In this talk we prove a Brunn-Minkowski inequality for the first Dirichlet eigenvalue of a Schrödinger type operator H ∶= − div(A ∇) + V, where V is convex and Kato decomposable, using the trace class property of the generated semigroup. As a consequence, using the ultracontractivity of thesemigroup we obtain the log-concavity of the…

In this talk, I will present some recent results and open problems about global regularity properties of classes of second order PDEs with non-negative characteristic form (e.g., sum-of-squares operators) that fail to satisfy the Hörmander condition, and nevertheless appear naturally in Several Complex Variables.Part of the results that I will present are joint with S.…