Wednesday May 15th, 2024 10:00 AM
to 11:00 AM
L4E48 and Zoom
Speaker: Professor Jana Björn, Linköping University and OIST TSVP Visiting Scholar
Title: The Dirichlet Problem and Boundary Regularity for Nonlinear Parabolic Equations
Abstract: As shown by Serrin in 1964, the growth at an isolated singularity of solutions to the elliptic equation div A(x, ∇u) = 0 in Rn (including p-harmonic functions with p > 1) is exactly determined by the dimension n and the parameter p associated with the equation. In this talk, I will discuss growth and integrability properties for p-harmonic Green functions and their gradients on weighted Rn, with a p-admissible weight, as well as on complete metric spaces equipped with a doubling measure supporting a p-Poincar´e inequality. In these situations, the dimension n is replaced by the local growth of the underlying measure near the isolated singularity, and the obtained growth and integrability exponents are sharp.