20 citations · 53 across the 46 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…
Trace and Hardy-Sobolev type inequalities and applications to a quasilinear elliptic problem in half-space
Loïc Constantin, Ranieri França Freire, Jacques Giacomoni
In the present paper we are dealing with the following quasilinear elliptic problem: \begin{equation*} \begin{cases} -\mathrm{div}(ρ(x_N) |\nabla u|^{p-2}\nabla u) =a|u|^{s-2}u &\m…
Multiplicity of solutions with prescribed mass for a quasilinear critical Choquard equation driven by a local-nonlocal operator
J. Giacomoni, Nidhi Nidhi, K. Sreenadh
In this paper we study the normalized solutions of the following critical growth Choquard equation with mixed local and non-local operators: \begin{equation*} \begin{array}{rcl} -Δ…
On Coron problems with Choquard term and mixed operator
Jacques Giacomoni, Tuhina Mukherjee, Lovelesh Sharma
In this article, we study a Coron-type problem involving a critical Choquard nonlinearity driven by a mixed operator combining the Laplacian and fractional Laplacian. In annular-ty…
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…