Tuesday, 23 October 2018, 3 p.m. (sharp),
prof. Carlos Jerez-Hanckes, Pontificia Universidad Catolica de Chile
at the conference room of IMATI-CNR in Pavia, will give a lecture titled:
High-order Galerkin method for Helmholtz and Laplace problems on multiple open arcs
and at 4 p.m.
Prof. Naian Liao, Chongqing University, Cina
will give a lecture titled:
Wiener-type boundary estimates for elliptic and parabolic equations
as part of the Applied Mathematics Seminar (IMATI-CNR e Dipartimento di Matematica, Pavia).
At the end a refreshment will be organized.
Abstract prof. Jerez-Hanckes. We present a spectral numerical scheme for solving Helmholtz and Laplace problems with Dirichlet boundary conditions on a finite collection of open arcs in $R^2$. An indirect boundary integral method is employed, giving rise to a first kind formulation whose variational form is discretized using weighted Chebyshev polynomials.
Well-posedness of both continuous and discrete problems is established as well as spectral convergence rates under the existence of analytic maps to describe the arcs. In order to reduce computation times, a simple matrix compression technique based on sparse kernel approximations is developed. Numerical results provided validate our claims.
Abstract prof. Liao. A beautiful geometric characterization of domains was established in the celebrate work of Norbert Wiener (1924) for the solvability of boundary value problem of harmonic functions.
In this talk, I will review some known results on Wiener's criterion for elliptic and parabolic equations. Estimates of modulus of continuity for solutions at the boundary will be given in terms of a Wiener-type integral, defined by a notion of capacity. In particular, some recent advances on such estimates for solutions to singular or degenerate parabolic equations will be reported.