Anup Biswas

activity

20232026

most citedLipschitz regularity of fractional

p

-Laplacian

1 citations · 1 across the 11 of their papers we have counts for

collaborators

12 papers

math.AP2026

Coercivity and regularity for nonlocal divergence-form operators with measurable kernels

Anup Biswas

We consider nonlocal divergence-form operators of the type $P V \int_{R^{n}} (u (x) - u (y)) K (x, y) d y = 0 in B_{2},$ where the kernel $K$ is symmetric ($K(x, y) = K(y…

math.AP2026

Hölder regularity and Harnack inequality for the logarithmic Laplacian

Anup Biswas, Subhajit Roy, Aniket Sen +1

In this article, we establish Schauder-type estimates for the logarithmic Laplacian. We show that for a $κ$ -Hölder inhomogeneous term, the solution is also $κ$ -Hölder in the interi…

math.AP2026

Strong comparison principle and symmetry results for the fractional $p$ -Laplacian

Anup Biswas, Subhajit Roy, Aniket Sen

In this article, we study the equation $(- Δ_{p})^{s} u = f (u)$ in a bounded domain $Ω \subset R^{n}$ , where $n \geq 2$ , $p > 2$ , and $f$ is locally Lipschitz. We establish a str…

math.AP2026

Lipschitz regularity for fractional $p$ -Laplacian with coercive gradients

Anup Biswas, Aniket Sen, Erwin Topp

In this article we study nonlinear nonlocal equations with coercive gradient nonlinearity of the form \[ (-Δ_{p})^{s}u(x)+H(x,\nabla u)=f , \] where $f$ is Lipschitz continuous and…

math.AP2025

Interior $C^{1, α}$ regularity of mixed local-nonlocal $(p, q)$ -energy minimizers for $p \leq s q$

Anup Biswas, Erwin Topp

We establish the local $C^{1, α}$ regularity of minimizers for functionals of the form $$w\to \int_Ω(|\nabla w|^p-fw) dx + \int_{\mathbb{R}^n}\int_{\mathbb{R}^n} \frac{|w(x)-w(y)|^…

math.AP2025

Liouville results for supersolutions of fractional $p$ -Laplacian equations with gradient nonlinearities

Mousomi Bhakta, Anup Biswas, Aniket Sen

We prove that any nonnegative viscosity solution of the inequality $(- Δ_{p})^{s} u (x) \geq u^{t} ∣\nabla u ∣^{m} in R^{N}, N \geq 2,$ must be constant. This re…

math.AP2025

Liouville results for $(p, q)$ -Laplacian elliptic equations with source terms involving gradient nonlinearities

Mousomi Bhakta, Anup Biswas, Roberta Filippucci

In this paper, we present a series of Liouville-type theorems for a class of nonhomogeneous quasilinear elliptic equations featuring reactions that depend on the solution and its g…

math.AP2025

Liouville properties for differential inequalities with $(p, q)$ Laplacian operator

Mousomi Bhakta, Anup Biswas, Roberta Filippucci

In this paper, we establish several Liouville-type theorems for a class of nonhomogenenous quasilinear inequalities. In the first part, we prove various Liouville results associate…

math.AP2025

Improved Hölder regularity of fractional $(p, q)$ -Poisson equation with regular data

Anup Biswas, Aniket Sen

We prove a quantitative Hölder continuity result for viscosity solutions to the equation $$ (-Δ_p)^{s}u(x) + {\rm PV} \int_{\mathbb{R}^n} |u(x)-u(x+z)|^{q-2}(u(x)-u(x+z))\frac{ξ(x,…

math.AP2025★ 1 cited

Lipschitz regularity of fractional $p$ -Laplacian

Anup Biswas, Erwin Topp

In this article, we investigate the Hölder regularity of the fractional $p$ -Laplace equation of the form $(- Δ_{p})^{s} u = f$ where $p > 1, s \in (0, 1)$ and $f \in L_{loc}^{\infty} (Ω)$ . S…

math.AP2024

Nonlocal Liouville theorems with gradient nonlinearity

Anup Biswas, Alexander Quaas, Erwin Topp

In this article we consider a large family of nonlinear nonlocal equations involving gradient nonlinearity and provide a unified approach, based on the Ishii-Lions type technique,…

math.AP2023

Nonlocal ergodic control problem in $R^{d}$

Anup Biswas, Erwin Topp

We study the existence-uniqueness of solution $(u, λ)$ to the ergodic Hamilton-Jacobi equation $(- Δ)^{s} u + H (x, \nabla u) = f - λ in R^{d},$ and $u \geq 0$ , whe…

Coercivity and regularity for nonlocal divergence-form operators with measurable kernels

Hölder regularity and Harnack inequality for the logarithmic Laplacian

Strong comparison principle and symmetry results for the fractional p-Laplacian

Lipschitz regularity for fractional p-Laplacian with coercive gradients

Interior C1,α regularity of mixed local-nonlocal (p,q)-energy minimizers for p≤sq

Liouville results for supersolutions of fractional p-Laplacian equations with gradient nonlinearities

Liouville results for (p,q)-Laplacian elliptic equations with source terms involving gradient nonlinearities

Liouville properties for differential inequalities with (p,q) Laplacian operator

Improved Hölder regularity of fractional (p,q)-Poisson equation with regular data

Lipschitz regularity of fractional p-Laplacian

Nonlocal Liouville theorems with gradient nonlinearity

Nonlocal ergodic control problem in Rd

Strong comparison principle and symmetry results for the fractional $p$ -Laplacian

Lipschitz regularity for fractional $p$ -Laplacian with coercive gradients

Interior $C^{1, α}$ regularity of mixed local-nonlocal $(p, q)$ -energy minimizers for $p \leq s q$

Liouville results for supersolutions of fractional $p$ -Laplacian equations with gradient nonlinearities

Liouville results for $(p, q)$ -Laplacian elliptic equations with source terms involving gradient nonlinearities

Liouville properties for differential inequalities with $(p, q)$ Laplacian operator

Improved Hölder regularity of fractional $(p, q)$ -Poisson equation with regular data

Lipschitz regularity of fractional $p$ -Laplacian

Nonlocal ergodic control problem in $R^{d}$