Starshapedness of the superlevel sets of solutions to equations involving the fractional Laplacian in starshaped rings

Sven Jarohs, Tadeusz Kulczycki and Paolo Salani

Mathematische Nachrichten, 2019, vol. 292, issue 5, 1008-1021

Abstract: We study solutions of the problem 0.1 −(−Δ)α/2u=f(x,u)inD0∖D¯1,u=0inRN∖D0,u=1inD¯1, where D1,D0⊂RN are open sets such that D¯1⊂D0, α∈(0,2), and f is a nonlinearity. Under different assumptions on f we prove that, if D0 and D1 are starshaped with respect to the same point x¯∈D¯1, then the same occurs for every superlevel set of u.

Date: 2019
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1002/mana.201700226

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:bla:mathna:v:292:y:2019:i:5:p:1008-1021

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0025-584X

Access Statistics for this article

Mathematische Nachrichten is currently edited by Robert Denk

More articles in Mathematische Nachrichten from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().