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math.AP2023★ 1 cited
On logarithmic double phase problems
Rakesh Arora, Ángel 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(e…
math.AP2023
Semiclassical Moser-Trudinger inequalities
Rakesh Arora, Phan Thành Nam, Phuoc-Tai Nguyen
We extend the Moser-Trudinger inequality of one function to systems of orthogonal functions. Our results are asymptotically sharp when applied to the collective behavior of eigenfu…