Papers by Carolina Mosquera
arXiv (Cornell University), Nov 12, 2021
In this paper we study the Dirichlet problem for systems of mean value equations on a regular tre... more 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.
Portugaliae Mathematica, 2014
We study evolution equations governed by an averaging operator on a directed tree, showing existe... more We study evolution equations governed by an averaging operator on a directed tree, showing existence and uniqueness of solutions. In addition we find conditions of the initial condition that allows us to find the asymptotic decay rate of the solutions as t → ∞. It turns out that this decay rate is not uniform, it strongly depends on how the initial condition goes to zero as one goes down in the tree.
Journal of the London Mathematical Society, 2014
In this paper we study the game p−Laplacian on a tree, that is, u(x) = α 2 max y∈S(x) u(y) + min ... more In this paper we study the game p−Laplacian on a tree, that is, u(x) = α 2 max y∈S(x) u(y) + min y∈S(x) u(y) + β m y∈S(x) u(y), here x is a vertex of the tree and S(x) is the set of successors of x. We study the family of the subsets of the tree that enjoy the unique continuation property, that is, subsets U such that u | U = 0 implies u ≡ 0.
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Papers by Carolina Mosquera