Explicit solutions for the Poisson problem in a ball for the logarithmic Laplacian

A. Ortega

doi:10.15330/cmp.18.1.111-116

Explicit solutions for the Poisson problem in a ball for the logarithmic Laplacian

Authors

A. Ortega National University of Distance Education, 14 Juan del Rosal str., 28040 Madrid, Spain https://orcid.org/0000-0003-1902-4275

https://doi.org/10.15330/cmp.18.1.111-116

Keywords:

logarithmic Laplacian, fundamental solution, Volterra function

Published online: 2026-05-15

Abstract

In this note, we introduce explicit formulas for the solution of the Poisson problem in a ball for the logarithmic Laplacian by means of semigroup theory and the Fourier transform. In particular, the solution for such problem is closely related to Volterra functions, which arise, for instance, in some convolution-type integral equations with logarithmic kernels.