10 papers
A unified approach to nonlinear Stein theorems
Arka Mallick, Swarnendu Sil
We study regularity for the variable exponent quasilinear -Laplace type equation on domains in Heisenberg groups and Euclidean spaces. We establish bord…
Leray-Trudinger Type Exponential Integrability in Log-Weighted Sobolev Spaces
Adimurthi, Sourav Ghosh, Arka Mallick
In this article, we conduct a comprehensive study of weighted Sobolev spaces with logarithmic weights, orginially introduced by Calanchi and Ruf to analyze the sharp exponential in…
Continuity estimates for variable growth variational problems in the Heisenberg group
Arka Mallick, Swarnendu Sil
We study regularity results for local minimizers of variable growth variational problem in Heisenberg groups under suitable integrability assumption on the horizontal gradient of t…
Excess decay for quasilinear equations in the Heisenberg group and consequences
Arka Mallick, Swarnendu Sil
We study regularity results for the solutions of quasilinear subelliptic -Laplace type equation in Heisenberg groups. We prove somewhat surprising excess decay estimates for the…
Gagliardo-Nirenberg Inequalities in Fractional Coulomb-Sobolev spaces for Radial functions
Arka Mallick, Hoai-Minh Nguyen
We extend the range of parameters associated with the Gagliardo-Nirenberg interpolation inequalities in the fractional Coulomb-Sobolev spaces for radial functions. We also study th…
The Caffarelli-Kohn-Nirenberg Inequalities For Radial Functions
Arka Mallick, Hoai-minh Nguyen
We establish the full range of the Caffarelli-Kohn-Nirenberg inequalities for radial functions in the Sobolev and the fractional Sobolev spaces of order . In particula…
Gagliardo-Nirenberg and Caffarelli-Kohn-Nirenberg interpolation inequalities associated with Sobolev-Coulomb spaces
Arka Mallick, Hoai-Minh Nguyen
We establish the full range Gagliardo-Nirenberg and the Caffarelli-Kohn-Nirenberg interpolation inequalities associated with Sobolev-Coulomb spaces for the (fractional) derivative…
Exponential integrability in the spirit of Moser-Trudinger's inequalities of functions with finite non-local, non-convex energy
Arka Mallick, Hoai-Minh Nguyen
Let , , and let be a smooth bounded open subset of . We prove some exponential integrability in the spirit of Moser-Trudinger's inequalities for…
On the Strong unique continuation property of a degenerate elliptic operator with Hardy type potential
Agnid Banerjee, Arka Mallick
In this paper we prove strong unique continuation for the following degenerate elliptic equation \begin{equation}\label{e0} Δ_zu +|z|^2\partial_t^2u = Vu,\quad (z,t) \in \mathbb{R}…
An Improved Leray-Trudinger Inequality
Arka Mallick, Cyril Tintarev
In this article, we have derived the following Leray-Trudinger type inequality on a bounded domain in containing the origin. \begin{align*} \displaystyle{\sup_{…