Il Giorno 16 ottobre 2024 si terranno i seguenti seminari  nell Sala riunioni II livello – Dip. Matematica e Applicazioni, Monte S. Angelo

ORARIO: 15:45-18

Prof. Maria Medina de La Torre – Universidad Autonoma de Madrid (UAM) (15:45-16:45)

Titolo: Asymptotic expansions and finite difference schemes for the fractional p-Laplacian

Abstract: We propose a new asymptotic expansion for the fractional p-Laplacian with precise computations of the errors, based on the idea that the singular part of the integral representation of the operator behaves like a local p-Laplacian with a weight correction. We also propose monotone finite difference approximations with explicit weights, and we obtain the associated error estimates.

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Prof. Jose Conde Alonso – Universidad Autonoma de Madrid (UAM) (17:00-18:00)

Title: Harmonic functions and the Bergman projection on general trees

Abstract: We study harmonic functions on quite general weighted trees. To do so, we study boundedness estimates for the Bergman projection, defined as a the real variable object that projects square-summable functions to the subspace of square-summable harmonic functions. We provide endpoint estimates for the Bergman projection, sparse-like domination results and weighted inequalities. A key difficulty that we encounter is the lack of regularity of the tree: we allow it to grow faster at each level in an unbounded fashion.

Based on joint work with Filippo De Mari (Genova), Matteo Monti (Bergamo), Elena Rizzo (Genova) and Maria Vallarino (Torino).