Work

The two membranes problem in a regular tree

Year: 2024

Type: article

Abstract: In this article, we study the two membranes problem for operators given in terms of a mean value formula on a regular tree. We show existence of solutions under adequate conditions on the boundary data and the involved source terms. We also show that, when the boundary data are strictly separated, the coincidence set is separated from the boundary and thus it contains only a finite number of nodes.

Source: Proceedings of the Royal Society of Edinburgh Section A Mathematics

DOI: 10.1017/prm.2024.137

Authors: Irene Gonzálvez, Alfredo Miranda, Julio D. Rossi

Institutions: Universidad Autónoma de Madrid, Universidad de Buenos Aires

Language: English

Topic: Differential Equations and Boundary Problems

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: European Commission, Consejo Nacional de Investigaciones Científicas y Técnicas, Secretaría de Ciencia y Técnica, Universidad de Buenos Aires, Agencia Estatal de Investigación