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Termine: Jeweils donnerstags, 13:45 - 15:15 im Raum HG 3.45

Anstehende Vorträge

On logarithmic p-Laplacian - Dr. Firoj Sk

In this talk, we introduce and analyze the logarithmic p-Laplacian \(L_{\Delta_p}\), a nonlocal operator of logarithmic order that arises as the formal derivative of the fractional p-Laplacian \((-\Delta_p)^s\) at s=0. This operator serves as a nonlinear extension of the recently developed logarithmic Laplacian operator. We present a variational framework to study Dirichlet problems involving  \(L_{\Delta_p}\) in bounded domains, which enables us to explore the relationship between the first Dirichlet eigenvalue and eigenfunction of both the fractional p-Laplacian and the logarithmic p-Laplacian. As a key result, we obtain a Faber–Krahn-type inequality for the first Dirichlet eigenvalue of  \(L_{\Delta_p}\). Additionally, we examine the validity of maximum and comparison principles, showing that these depend on the sign of the first Dirichlet eigenvalue of   \(L_{\Delta_p}\). Finally, we discuss a boundary Hardy-type inequality for the spaces associated with the weak formulation of the logarithmic p-Laplacian.

The talk is based on joint work with B. Dyda and S. Jarohs.