Wiener-type boundary estimates for elliptic and parabolic equations
Prof. Naian Liao, Chongqing University, Cina
Sala conferenze IMATI-CNR, Pavia - Tuesday, October 23, 2018 h.16:00
Abstract. 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.
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