3 papers
math.AP2025
Sharp embeddings and existence results for Logarithmic -Laplacian equations with critical growth
Rakesh Arora, Jacques Giacomoni, Hichem Hajaiej +1
In this paper, we derive a new -Logarithmic Sobolev inequality and optimal continuous and compact embeddings into Orlicz-type spaces of the function space associated with the lo…
math.AP2025
The Brezis-Nirenberg and logistic problem for the Logarithmic Laplacian
Rakesh Arora, Jacques Giacomoni, Arshi Vaishnavi
In this work, we study the non-local analogue of Brezis-Nirenberg and logistic type elliptic equations involving the logarithmic Laplacian and critical logarithmic non-linearity wi…
math.AP2024
Nonlocal elliptic equations involving logarithmic Laplacian: Existence, non-existence and uniqueness results
Rakesh Arora, Jacques Giacomoni, Arshi Vaishnavi
In this work, we study the existence, non-existence, and uniqueness results for nonlocal elliptic equations involving logarithmic Laplacian, and subcritical, critical, and supercri…