3 papers
math.AP2026
On the FuÄÃk spectrum of the Logarithmic Laplacian
Rakesh Arora, Tuhina Mukherjee
In this paper, we investigate the FuÄÃk spectrum associated with the logarithmic Laplacian. This spectrum is defined as the set of all pairs for…
math.AP2025
Logarithmic double phase problems with generalized critical growth
Rakesh Arora, Ãngel Crespo-Blanco, Patrick Winkert
In this paper we study logarithmic double phase problems with variable exponents involving nonlinearities that have generalized critical growth. We first prove new continuous and c…
math.AP2025
On logarithmic double phase problems
Rakesh Arora, Ãngel Crespo-Blanco, Patrick Winkert
In this paper we introduce a new logarithmic double phase type operator of the form\begin{align*}\mathcal{G}u:=-\operatorname{div}\left(|\nabla u|^{p(x)-2}\nabla u+μ(x)\left[\log(…