20 citations · 53 across the 46 of their papers we have counts for
50 papers
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…