Geometry and Geometric Analysis Working Group

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The asymptotic p-Poisson equation as p → ∞ in Carnot--Carathéodory spaces

Speaker: Simone Verzellesi, University of Trento

Location: Warren Weaver Hall 1314

Date: Tuesday, March 21, 2023, 11 a.m.

Synopsis:

In a celebrated paper of the late 80s, T. Bhattacharya, E. DiBenedetto and J. Manfredi obtained solutions to the Dirichlet problem associated to the infinite Laplace operator as suitable limits of \(p\)-harmonic functions. This approach built a bridge between many notions of solutions to the aforementioned problem, such as e.g. viscosity solutions, variational solutions and absolutely minimizing Lipschitz extensions. In this talk, after an introduction to the problem in the Euclidean setting, we generalize this perspective to the framework of Carnot-Carathéodory spaces, highlighting the main difficulties that the new anisotropic framework let arise. This seminar is based on recent papers with L. Capogna, G. Giovannardi, A. Pinamonti and C. Wang.