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math.AP2026
The Fractional-Logarithmic Laplacian: Fundamental Properties and Eigenvalues
Huyuan Chen, Rui Chen, Daniel Hauer
In this paper, we introduce the fractional--logarithmic Laplacian \( (-Δ)^{s+\log} \), defined as the derivative of the fractional Laplacian \( (-Δ)^t \) at \(t=s\). It is a singul…
math.AP2025
A multi-point maximum principle to prove global Harnack inequalities for Schrödinger operators
Ben Andrews, Daniel Hauer, Jessica Slegers
In this article, we introduce a new methodology to prove global parabolic Harnack inequalities on Riemannian manifolds. We focus on presenting a new proof of the global pointwise H…
math.AP2023★ 2 cited
An extension problem for the logarithmic Laplacian
Huyuan Chen, Daniel Hauer, Tobias Weth
The logarithmic Laplacian on the (whole) N-dimensional Euclidean space is defined as the first variation of the fractional Laplacian of order 2s at s=0 or, alternatively, as a sing…