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Systems involving mean value formulas on trees
Part of:
Low-dimensional dynamical systems
Potential theory on metric spaces
Miscellaneous topics - Partial differential equations
Elliptic equations and systems
Published online by Cambridge University Press: 03 January 2024
Abstract
In this paper, we study the Dirichlet problem for systems of mean value equations on a regular tree. We deal both with the directed case (the equations verified by the components of the system at a node in the tree only involve values of the unknowns at the successors of the node in the tree) and the undirected case (now the equations also involve the predecessor in the tree). We find necessary and sufficient conditions on the coefficients in order to have existence and uniqueness of solutions for continuous boundary data. In a particular case, we also include an interpretation of such solutions as a limit of value functions of suitable two-players zero-sum games.
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- © The Author(s), 2024. Published by Cambridge University Press on behalf of Canadian Mathematical Society
Footnotes
C. Mosquera is partially supported by grants UBACyT 20020170100430BA (Argentina), PICT 2018–03399 (Argentina), and PICT 2018–04027 (Argentina). A. Miranda and J. Rossi are partially supported by grants CONICET grant PIP GI No. 11220150100036CO (Argentina), PICT-2018-03183 (Argentina), and UBACyT grant 20020160100155BA (Argentina).
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