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The two membranes problem in a regular tree

Published online by Cambridge University Press:  27 December 2024

Irene Gonzálvez Open the ORCID record for Irene Gonzálvez [Opens in a new window] ,
Alfredo Miranda Open the ORCID record for Alfredo Miranda [Opens in a new window]  and
Julio D. Rossi Open the ORCID record for Julio D. Rossi [Opens in a new window]
Irene Gonzálvez*
Affiliation:
Departamento de Matemáticas, Universidad Autónoma de Madrid, Campus de Cantoblanco, 28049 Madrid, Spain ([email protected]) (corresponding author)
Alfredo Miranda
Affiliation:
Departamento de Matemáticas, FCEyN, Universidad de Buenos Aires, Pabellón I, Ciudad Universitaria (1428), Buenos Aires, Argentina ([email protected], [email protected])
Julio D. Rossi
Affiliation:
Departamento de Matemáticas, FCEyN, Universidad de Buenos Aires, Pabellón I, Ciudad Universitaria (1428), Buenos Aires, Argentina ([email protected], [email protected])
*
*Corresponding author.
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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.

Keywords

two membranes problemregular treemean value operatorsgame theoryobstacle problem
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , First View , pp. 1 - 30
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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