7 papers
Global Calderon-Zygmund estimates for irregular double-phase evolution problem with non-divergence data
Rakesh Arora, Sergey Shmarev
We study irregular double-phase parabolic equations with variable exponents and non-divergence data, \[ u_t-\operatorname{div} \left(\mathcal{F}(z,\nabla u)\nabla u \right)=f(z),\q…
Spectral Properties of the Logarithmic Laplacian with Indefinite Weights
Rakesh Arora, Tuhina Mukherjee, Arshi Vaishnavi
In this paper, we investigate a weighted eigenvalue problem driven by the Logarithmic Laplacian with indefinite weights. We prove the existence of an unbounded sequence of Lusterni…
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…
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…
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…
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…