Swarnendu Sil

activity

20172026

most citedLimiting absorption principle and well-posedness for the time-harmonic Maxwell equations with anisotropic sign-changing coefficients

15 citations · 54 across the 13 of their papers we have counts for

collaborators

16 papers

math.AP2026

A unified approach to nonlinear Stein theorems

Arka Mallick, Swarnendu Sil

We study regularity for the variable exponent quasilinear $p (x)$ -Laplace type equation on domains in Heisenberg groups and Euclidean spaces. We establish bord…

math.AP2026

Gradient estimates for $p (\cdot)$ -harmonic differential forms

Anna Balci, Swarnendu Sil, Mikhail Surnachev

In this paper, we establish gradient bounds for $p (\cdot)$ -harmonic differential forms subject to a Coulomb-type gauge condition. For variable exponents satisfying the log-Hölder c…

math.AP2026

Weighted estimates for Hodge-Maxwell systems

Rohit Mahato, Swarnendu Sil

We establish up to the boundary regularity estimates in weighted $L^{p}$ spaces with Muckenhoupt weights $A_{p}$ for weak solutions to the Hodge systems \begin{align*} d^{\ast}\lef…

math.AP2025

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…

math.AP2024

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 $p$ -Laplace type equation in Heisenberg groups. We prove somewhat surprising excess decay estimates for the…

math.AP2024

Morrey-Lorentz estimates for Hodge-type systems

Banhirup Sengupta, Swarnendu Sil

We prove up to the boundary regularity estimates in Morrey-Lorentz spaces for weak solutions of the linear system of differential forms with regular anisotropic coefficients \begin…

math.DG2024

Topology and approximation of weak $G$ -bundles in the supercritical dimensions

Swarnendu Sil

For analyzing stationary Yang-Mills connections in higher dimensions, one has to work with Morrey-Sobolev bundles and connections. The transition maps for a Morrey-Sobolev principa…

math.AP2023

BMO estimates for Hodge-Maxwell systems with discontinuous anisotropic coefficients

Dharmendra Kumar, Swarnendu Sil

We prove up to the boundary $BMO$ estimates for linear Maxwell-Hodge type systems for $R^{N}$ -valued differential $k$ -forms $u$ in $n$ dimensions \begin{align*} \…

math.AP2019★ 15 cited

Limiting absorption principle and well-posedness for the time-harmonic Maxwell equations with anisotropic sign-changing coefficients

Hoai Minh Nguyen, Swarnendu Sil

We study the limiting absorption principle and the well-posedness of Maxwell equations with anisotropic sign-changing coefficients in the time-harmonic domain. The starting point o…

math.DG2019★ 1 cited

Topology of weak $G$ -bundles via Coulomb gauges in critical dimensions

Swarnendu Sil

The transition maps for a Sobolev $G$ -bundle are not continuous in the critical dimension and thus the usual notion of topology does not make sense. In this work, we show that if s…

math.AP2018

Nonlinear Stein theorem for differential forms

Swarnendu Sil

We prove that if $u$ is an $R^{N}$ -valued $W_{l oc}^{1, p}$ differential $k$ -form with $δ (a (x) ∣ d u ∣^{p - 2} d u) \in L_{l oc}^{(n, 1)}$ in a domain of $\…

math.FA2017★ 6 cited

Calculus of Variations: A Differential Form Approach

Swarnendu Sil

We study integrals of the form $\int_{Ω} f (d ω_{1}, \dots, d ω_{m}),$ where $m \geq 1$ is a given integer, $1 \leq k_{i} \leq n$ are integers and $ω_{i}$ is a $(k_{i} - 1)$ -f…

math.FA2017★ 14 cited

On the best constant in {G}affney inequality

Gyula Csato, Bernard Dacorogna, Swarnendu Sil

We discuss the value of the best constant in Gaffney inequality namely $$ \lVert \nabla ω\rVert_{L^{2}}^{2}\leq C\left( \lVert dω\rVert_{L^{2}}^{2}+\lVert δω\rVert_{L^{2}% }^{2}+\l…

math.FA2017★ 1 cited

Notions of affinity in calculus of variations with differential forms

Saugata Bandyopadhyay, Swarnendu Sil

Ext-int.\ one affine functions are functions affine in the direction of one-divisible exterior forms, with respect to exterior product in one variable and with respect to interior…

math.FA2017★ 6 cited

Exterior convexity and classical calculus of variations

Saugata Bandyopadhyay, Swarnendu Sil

We study the relation between various notions of exterior convexity introduced in Bandyopadhyay-Dacorogna-Sil \cite{BDS1} with the classical notions of rank one convexity, quasicon…

math.FA2017★ 11 cited

Calculus of Variations with Differential Forms

Saugata Bandyopadhyay, Bernard Dacorogna, Swarnendu Sil

We study integrals of the form $\int_{Ω} f (d ω)$ , where $1 \leq k \leq n$ , $f : Λ^{k} \to R$ is continuous and $ω$ is a $(k - 1)$ -form. We introduce the…

A unified approach to nonlinear Stein theorems

Gradient estimates for p(⋅)-harmonic differential forms

Weighted estimates for Hodge-Maxwell systems

Continuity estimates for variable growth variational problems in the Heisenberg group

Excess decay for quasilinear equations in the Heisenberg group and consequences

Morrey-Lorentz estimates for Hodge-type systems

Topology and approximation of weak G-bundles in the supercritical dimensions

BMO estimates for Hodge-Maxwell systems with discontinuous anisotropic coefficients

Limiting absorption principle and well-posedness for the time-harmonic Maxwell equations with anisotropic sign-changing coefficients

Topology of weak G-bundles via Coulomb gauges in critical dimensions

Nonlinear Stein theorem for differential forms

Calculus of Variations: A Differential Form Approach

On the best constant in {G}affney inequality

Notions of affinity in calculus of variations with differential forms

Exterior convexity and classical calculus of variations

Calculus of Variations with Differential Forms

Gradient estimates for $p (\cdot)$ -harmonic differential forms

Topology and approximation of weak $G$ -bundles in the supercritical dimensions

Topology of weak $G$ -bundles via Coulomb gauges in critical dimensions