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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…
Irregular double-phase evolution problem: existence and global regularity
Rakesh Arora, Sergey Shmarev
We investigate the homogeneous Dirichlet problem for the irregular double-phase evolution equation \[ u_t-\operatorname{div} \left( a(z)|\nabla u|^{p(z)-2} \nabla u + b(z)|\nabla u…
Global Existence and Finite-Time Blow-Up of Solutions for Parabolic Equations Involving the Fractional Musielak -Laplacian
Rakesh Arora, Anouar Bahrouni, Nitin Kumar Maurya
In this work, we study the parabolic fractional Musielak -Laplacian equation: \begin{equation*} \left\{ \begin{aligned} u_{t} + (-Δ)_{{g}_{x,y}}^{s} u &= f(x,u), && \text{…
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…