Analysis & Applications Seminar
End-point maximal regularity for the discrete parabolic Cauchy problem and regularity of non-local operators in discrete Besov spaces
Speaker: Marta de León Contreras (Universidad de la Laguna)Date: Friday, 30 January 2026 - 11:30Place: Aula Gris 2, ICMAT
Abstract:
In the study of partial differential equations, it is desirable to get some regularity results for the differential operators involved, as well as a priori estimates for the solutions, which provide information about the smoothness of the solutions before even solving the equation. In particular, it is quite interesting to study for which operators the los of regularity phenomenon does not hold or, equivalently, when an operator has the maximal regularity property. In this talk we shall show that, thanks to the semigroup language, in the case of the discrete Laplacian operator we can obtain end-point maximal L^1-regularity for the discrete parabolic Cauchy problem as well as other regularity properties for fractional powers of the discrete Laplacian in discrete Besov spaces.
The content of this talk is based on joint work with L. Abadias and A. Mahillo.
