An elliptic problem of the Prandtl–Batchelor type with a singularity

Choudhuri, Debajyoti (author), Repovš, Dušan (author)

We establish the existence of at least two solutions of the Prandtl–Batchelor like elliptic problem driven by a power nonlinearity and a singular term. The associated energy functional is nondifferentiable, and hence the usual variational techniques do not work. We shall use a novel approach in tackling the associated energy functional by a sequence of $C^1$ functionals and a cutoff function. Our main tools are fundamental elliptic regularity theory and the mountain pass theorem.

• Language: English
• Keywords: elliptic free boundary problems, mountain pass theorem, singularity
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2023
• Number of pages: 18 str.
• Numbering: Vol. 2023, art. 63
• PID: 20.500.12556/RUL-147075
• UDC: 517.9
• ISSN on article: 1687-2770
• DOI: 10.1186/s13661-023-01747-w
• COBISS.SI-ID: 156397059
• Publication date in RUL: 22.06.2023

Record is a part of a journal

• Title: Boundary value problems
• Shortened title: Bound. value probl.
• Publisher: Springer Nature
• ISSN: 1687-2770
• COBISS.SI-ID: 62113025

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.