Liouville type results for the fractional truncated Laplacians in a half-space

TL;DR

This paper investigates the existence of viscosity supersolutions for nonlinear integral equations involving fractional truncated Laplacians in a half-space, aiming to identify critical exponents that distinguish between existence and nonexistence.

Contribution

It provides new Liouville type results for fractional truncated Laplacians in a half-space, establishing thresholds for the existence of solutions.

Findings

Identified critical exponents separating existence and nonexistence regimes.

Derived estimates for viscosity supersolutions in the half-space.

Extended Liouville theorems to fractional truncated Laplacian operators.

Abstract

Existence issues of viscosity supersolutions in the half-space $\mathbb R^N_+$, for a class of fully nonlinear integral equations involving the fractional truncated Laplacians and a power-like nonlinearity in the unknown function, are addressed in this paper, the aim being to obtain estimates on the threshold exponents separating the existence from the nonexistence regimes.