A direct method of moving planes for fully nonlinear nonlocal operators and applications

Yuxia Guo; Shaolong Peng

doi:10.3934/DCDSS.2020462

A direct method of moving planes for fully nonlinear nonlocal operators and applications

Yuxia Guo^*
, Shaolong Peng

^*Corresponding author for this work

Tsinghua University

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In this paper, we are concerned with the following generalized fully nonlinear nonlocal operators: Fs;m(u(x)) = cN;sm N2 +sP:V: Z RN G(u(x) - u(y)) lx - yl N2 +s KN2 +s(mlx-yl)dy+m2su(x); where s 2 (0; 1) and mass m > 0. By establishing various maximal principle and using the direct method of moving plane, we prove the monotonicity, symmetry and uniqueness for solutions to fully nonlinear nonlocal equation in unit ball, RN, RN+ and a coercive epigraph domain in RN respectively.

Original language	English
Pages (from-to)	1871-1897
Number of pages	27
Journal	Discrete and Continuous Dynamical Systems - Series S
Volume	14
Issue number	6
DOIs	https://doi.org/10.3934/DCDSS.2020462
State	Published - Jun 2021
Externally published	Yes

Keywords

Direct methods of moving planes
Fully nonlinear nonlocal operators
Liouville theorem
Maximal principle
Symmetry and Monotonicity

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10.3934/DCDSS.2020462

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abstract = "In this paper, we are concerned with the following generalized fully nonlinear nonlocal operators: Fs;m(u(x)) = cN;sm N2 +sP:V: Z RN G(u(x) - u(y)) lx - yl N2 +s KN2 +s(mlx-yl)dy+m2su(x); where s 2 (0; 1) and mass m > 0. By establishing various maximal principle and using the direct method of moving plane, we prove the monotonicity, symmetry and uniqueness for solutions to fully nonlinear nonlocal equation in unit ball, RN, RN+ and a coercive epigraph domain in RN respectively.",

keywords = "Direct methods of moving planes, Fully nonlinear nonlocal operators, Liouville theorem, Maximal principle, Symmetry and Monotonicity",

author = "Yuxia Guo and Shaolong Peng",

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month = jun,

doi = "10.3934/DCDSS.2020462",

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AU - Guo, Yuxia

AU - Peng, Shaolong

PY - 2021/6

Y1 - 2021/6

N2 - In this paper, we are concerned with the following generalized fully nonlinear nonlocal operators: Fs;m(u(x)) = cN;sm N2 +sP:V: Z RN G(u(x) - u(y)) lx - yl N2 +s KN2 +s(mlx-yl)dy+m2su(x); where s 2 (0; 1) and mass m > 0. By establishing various maximal principle and using the direct method of moving plane, we prove the monotonicity, symmetry and uniqueness for solutions to fully nonlinear nonlocal equation in unit ball, RN, RN+ and a coercive epigraph domain in RN respectively.

AB - In this paper, we are concerned with the following generalized fully nonlinear nonlocal operators: Fs;m(u(x)) = cN;sm N2 +sP:V: Z RN G(u(x) - u(y)) lx - yl N2 +s KN2 +s(mlx-yl)dy+m2su(x); where s 2 (0; 1) and mass m > 0. By establishing various maximal principle and using the direct method of moving plane, we prove the monotonicity, symmetry and uniqueness for solutions to fully nonlinear nonlocal equation in unit ball, RN, RN+ and a coercive epigraph domain in RN respectively.

KW - Direct methods of moving planes

KW - Fully nonlinear nonlocal operators

KW - Liouville theorem

KW - Maximal principle

KW - Symmetry and Monotonicity

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DO - 10.3934/DCDSS.2020462

M3 - 文章

AN - SCOPUS:85108851931

SN - 1937-1632

VL - 14

SP - 1871

EP - 1897

JO - Discrete and Continuous Dynamical Systems - Series S

JF - Discrete and Continuous Dynamical Systems - Series S

IS - 6

ER -

A direct method of moving planes for fully nonlinear nonlocal operators and applications

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Keywords

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