Anup Biswas

collaborators

10 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.AP2026

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

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

Anup Biswas, Erwin Topp

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

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

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

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

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

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

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