Geodesic
Systems involving mean value formulas on trees
Canadian journal of mathematics, Tome 77 (2025) no. 2, pp. 351-383

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DOI

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.
DOI : 10.4153/S0008414X23000913
Mots-clés : Regular trees, systems, mean value formula 
Miranda, Alfredo; Mosquera, Carolina A.; Rossi, Julio D. Systems involving mean value formulas on trees. Canadian journal of mathematics, Tome 77 (2025) no. 2, pp. 351-383. doi: 10.4153/S0008414X23000913
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     title = {Systems involving mean value formulas on trees},
     journal = {Canadian journal of mathematics},
     pages = {351--383},
     year = {2025},
     volume = {77},
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     doi = {10.4153/S0008414X23000913},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X23000913/}
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