Anup Biswas

collaborators

6 papers

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

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…

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

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