Methods of the Perturbation Theory for Fundamental Solutions to the Generalization of the Fractional Laplaciane

Mykola Ivanovich Yaremenko

A chapter in Numerical Simulation - Advanced Techniques for Science and Engineering from IntechOpen

Abstract: We study the regularity properties of the solutions to the fractional Laplacian equation with perturbations. The Harnack inequality of a weak solution u?WspRl to the fractional Laplacian problem is established, and the oscillation of the solution to the fractional Laplacian is estimated. We show that let 1

Keywords: Holder continuous; partial differential equation; perturbation method; analysis; calculus; mathematics; function; functional analysis; Harnack inequality; Sobolev space; singular integrals; differentiability class; semigroup; interpolation theorem; fractional Laplacian; partial differential equation; Holder inequality; Laplace operator; general solution; regularity; nonlocal model (search for similar items in EconPapers)
JEL-codes: C60 (search for similar items in EconPapers)
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.intechopen.com/chapters/85796 (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ito:pchaps:303021

DOI: 10.5772/intechopen.109366

Access Statistics for this chapter

More chapters in Chapters from IntechOpen
Bibliographic data for series maintained by Slobodan Momcilovic ().