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Next talk of the Seminar (14:00, Room Sousa Pinto)
12/12/2025: “Regularity Estimates for Zeroth Order Operators”
Héctor Chang-Lara (Universidade de Coimbra)
A
very interesting limit case of the fractional Laplacian in  is given by
which serves as a principal example of a zeroth-order
integro-differential operator. This operator
arises naturally as the leading term of the logarithmic Laplacian which has
been studied in recent years. In contrast with the fractional Laplacian,
the scaling properties in this scenario are very delicate, in particular
the dilation of the kernel leads to a non-integrable tail which represents
a challenge for the regularity theory of solutions of equations governed by
 .
In this talk, I will present interior continuity estimates for solutions to
a family of operators comparable to the one above, obtained in
collaboration with Alberto Saldaña.
This seminar is supported in part by CIDMA under the Portuguese
Foundation for Science and Technology (FCT, https://ror.org/00snfqn58)
Multi-Annual Financing Program for R&D Units, grants UID/4106/2025 and
UID/PRR/4106/2025.
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