Palestras e Seminários
21/08/2025
14:00
Online / à distância
Palestrante: Julio D. Rossi
https://sites.google.com/usp.br/evol-eq-and-dyn-systems
Responsável: Estefani Moraes Moreira (estefani@usp.br)
Webinar on Evolution Equations and Dynamical Systems
Resumo:In this talk we will introduce two new fractional operators. The first one is based on the classical formula that writes the usual Laplacian as the sum of the eigenvalues of the Hessian. The second one comes from looking at the classical fractional Laplacian as the mean value (in the sphere) of the 1-dimensional fractional Laplacians in lines with directions in the sphere. To obtain this second new fractional operator we just replace the mean value by the mid-range of 1-dimensional fractional Laplacians with directions in the sphere.
For these two new fractional operators we prove a comparison principle for viscosity sub and supersolutions and then we obtain existence and uniqueness for the Dirichlet problem. Finally, we prove that for the first operator we recover the classical Laplacian in the limit as $s$ goes to 1.
Joint work with Jorge Ruiz-Cases (UAM, Madrid).
For these two new fractional operators we prove a comparison principle for viscosity sub and supersolutions and then we obtain existence and uniqueness for the Dirichlet problem. Finally, we prove that for the first operator we recover the classical Laplacian in the limit as $s$ goes to 1.
Joint work with Jorge Ruiz-Cases (UAM, Madrid).
Link: No site