Aniket Sen

collaborators

5 papers

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 $(- I^_{p})^{s} u = f (u)$ in a bounded domain $I^c ◯ \subset R^{n}$ , where $n \geq 2$ , $p > 2$ , and $f$ is locally Lipschitz. We establish a s…

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 \[ (-Î_p)^s u(x) + H(x, \nabla u) = f, \] where $f$ is Lipschitz continuous.…

math.AP2026

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 $(- I^_{p})^{s} u (x) \geq u^{t} ∣\nabla u ∣^{m} in R^{N}, N \geq 2,$ must be constant. This r…

math.AP2025

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

Anup Biswas, Aniket Sen

We prove a quantitative HÃ¶lder continuity result for viscosity solutions to the equation $$ (-Î_p)^{s}u(x) + {\rm PV} \int_{\mathbb{R}^n} |u(x)-u(x+z)|^{q-2}(u(x)-u(x+z))\frac{Î¾…

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

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

Improved HÃ¶lder regularity of fractional (p,q)-Poisson equation with regular data

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

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

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

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