Global higher regularity and decay estimates for positive solutions of fractional equations in RN *

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED Nonlinearity Pub Date : 2024-05-10 DOI:10.1088/1361-6544/ad4503

Yinbin Deng, Xian Yang

引用次数: 0

Abstract

In the paper, we study the global higher regularity and decay estimates of the positive solutions for the following fractional equations

{(−Δ)su+u=|u|p−2uin RN,lim|x|→∞u(x)=0,u∈Hs(RN),(0.1)

where

s∈(0,1)

N>2s

2<p<2s∗:=2NN−2s

and

(−Δ)s

is the fractional Laplacian. Let Q be a positive solution of (). We prove that

Q∈Ck,γ(RN)∩Hk(RN)

and obtain the decay estimates of D ^k Q as

|x|→∞

for all

k∈N+

and

γ∈(0,1)

. The argument relies on the Bessel kernel, comparison principle, Fourier analysis and iteration methods.

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RN 中分式方程正解的全局高正则性和衰减估计 *

本文研究下列分式方程 {(-Δ)su+u=|u|p-2uin RN,lim|x|→∞u(x)=0,u∈Hs(RN),(0.1) 其中 s∈(0,1), N>2s, 2<p<2s∗:=2NN-2s 且 (-Δ)s 为分数拉普拉奇。设 Q 为 () 的正解。我们证明 Q∈Ck,γ(RN)∩Hk(RN)，并得到 DkQ 在所有 k∈N+ 和 γ∈(0,1) 条件下的|x|→∞衰减估计值。论证依赖于贝塞尔核、比较原理、傅里叶分析和迭代方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Nonlinearity 物理-物理：数学物理

CiteScore

3.00

自引率

5.90%

发文量

170

审稿时长

12 months

期刊介绍： Aimed primarily at mathematicians and physicists interested in research on nonlinear phenomena, the journal''s coverage ranges from proofs of important theorems to papers presenting ideas, conjectures and numerical or physical experiments of significant physical and mathematical interest. Subject coverage: The journal publishes papers on nonlinear mathematics, mathematical physics, experimental physics, theoretical physics and other areas in the sciences where nonlinear phenomena are of fundamental importance. A more detailed indication is given by the subject interests of the Editorial Board members, which are listed in every issue of the journal. Due to the broad scope of Nonlinearity, and in order to make all papers published in the journal accessible to its wide readership, authors are required to provide sufficient introductory material in their paper. This material should contain enough detail and background information to place their research into context and to make it understandable to scientists working on nonlinear phenomena. Nonlinearity is a journal of the Institute of Physics and the London Mathematical Society.

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