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

2025/11/09 by Bhakta, Mousomi, Biswas, Anup, Sen, Aniket
Mathematics · #Nonlinear Partial Differential Equations #Geometric Analysis and Curvature Flows #Nonlinear Differential Equations Analysis

paper · doi:10.48550/arxiv.2511.06334

Abstract

We prove that any nonnegative viscosity solution of the inequality (-Δ_p)^s u(x) ≥ u^t |∇ u|^m in ℝ^N, N≥ 2, must be constant. This result holds for parameters p∈ (1, ∞), s∈ (0, 1), t, m≥ 0, satisfying t (N-sp) + m(N-(sp-p+1)) lt; N(p-1), with the additional condition that either m≤ p-1 if p-1

Citations

• Liouville properties for differential inequalities with (p,q) Laplacian operator
• Lipschitz regularity of fractional p-Laplacian
• Nonlocal Liouville theorems with gradient nonlinearity
• Bernstein theorems for nonlinear geometric PDEs
• Higher Hölder regularity for the fractional p-Laplace equation in the subquadratic case
• The fundamental solution of the fractional p-laplacian
• Hölder regularity and Liouville properties for nonlinear elliptic inequalities with power-growth gradient terms
• On the Liouville property for fully nonlinear equations with superlinear first-order terms
• Liouville-type theorems and existence of solutions for quasilinear elliptic equations with nonlinear gradient terms
• Equivalence of weak and viscosity solutions in fractional\n non-homogeneous problems
• Liouville results for fully nonlinear equations modeled on H "ormander\n vector fields. I. The Heisenberg group
• Higher H "older regularity for the fractional p-Laplacian in the\n superquadratic case
• Equivalence of solutions to fractional p-Laplace type equations
• Liouville properties and critical value of fully nonlinear elliptic\n operators

Related

• Liouville type results for the fractional truncated Laplacians in a half-space
• On the Liouville property for fully nonlinear equations with superlinear first-order terms
• Equivalence of solutions to fractional p-Laplace type equations
• H "older estimates for viscosity solutions of equations of fractional\n p-Laplace type
• Lower semicontinuity and pointwise behavior of supersolutions for some doubly nonlinear nonlocal parabolic p-Laplace equations