Open AccessMonotonicity results for the fractional p-Laplacian in unbounded domains
Author(s) -
Leyun Wu,
Mei Yu,
Binlin Zhang
Publication year - 2021
Publication title -
bulletin of mathematical sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.407
H-Index - 21
eISSN - 1664-3607
pISSN - 1664-3615
DOI - 10.1142/s166436072150003x
Subject(s) - monotonic function , fractional laplacian , mathematics , conjecture , infinity , laplace operator , nonlinear system , sequence (biology) , fractional calculus , pure mathematics , work (physics) , mathematical analysis , combinatorics , physics , quantum mechanics , biology , genetics , thermodynamics
In this paper, we develop a direct method of moving planes in unbounded domains for the fractional p-Laplacians, and illustrate how this new method to work for the fractional p-Laplacians. We first proved a monotonicity result for nonlinear equations involving the fractional p-Laplacian in [Formula: see text] without any decay conditions at infinity. Second, we prove De Giorgi conjecture corresponding to the fractional p-Laplacian under some conditions. During these processes, we introduce some new ideas: (i) estimating the singular integrals defining the fractional p-Laplacian along a sequence of approximate maxima; (ii) estimating the lower bound of the solutions by constructing sub-solutions.