Moving planes and sliding methods for fractional elliptic and parabolic equations

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Abstract: In this paper, we summarize some of the recent developments in the area of fractional elliptic and parabolic equations with focus on how to apply the sliding method and the method of moving planes to obtain qualitative properties of solutions. We will compare the two methods and point out the pros and cons of each. We will demonstrate how to modify the ideas and techniques in studying fractional elliptic equations and then to employ them to investigate fractional parabolic problems. Besides deriving monotonicity of solutions, some other applications of the sliding method will be illustrated. These results have more or less appeared in a series of previous literatures, in which the ideas were usually submerged in detailed calculations. What we are trying to do here is to single out these ideas and illuminate the inner connections among them by using figures and intuitive languages, so that the readers can see the whole picture and quickly grasp the essence of these useful methods and will be able to apply them to solve a variety of other fractional elliptic and parabolic problems.

Standort
Deutsche Nationalbibliothek Frankfurt am Main
Umfang
Online-Ressource
Sprache
Englisch

Erschienen in
Moving planes and sliding methods for fractional elliptic and parabolic equations ; volume:24 ; number:2 ; year:2024 ; pages:359-398 ; extent:40
Advanced nonlinear studies ; 24, Heft 2 (2024), 359-398 (gesamt 40)

Urheber
Chen, Wenxiong
Hu, Yeyao
Ma, Lingwei

DOI
10.1515/ans-2022-0069
URN
urn:nbn:de:101:1-2404181705279.243134786282
Rechteinformation
Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
Letzte Aktualisierung
14.08.2025, 10:51 MESZ

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Beteiligte

  • Chen, Wenxiong
  • Hu, Yeyao
  • Ma, Lingwei

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