2 citations · 6 across the 20 of their papers we have counts for
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On the classification of solutions to the Logarithmic Laplacian critical Choquard equation
Rakesh Arora, Jacques Giacomoni
In this work, we establish a sharp logarithmic Choquard inequality by combining Beckner's entropy inequality with the sharp Pitt-type inequality. Motivated by this estimate, we cla…
On fractional -Laplacian evolution equation
Rakesh Arora, Nitin Kumar Maurya
We study a nonlocal evolution problem driven by the fractional -Laplacian with a Carathéodory nonlinearity satisfying subcritical growth conditions. We develop a potential well…
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…