info:eu-repo/semantics/article
Convex Envelopes on Trees
Fecha
2020-11Registro en:
del Pezzo, Leandro Martin; Frevenza Maestrone, Nicolas Federico; Rossi, Julio Daniel; Convex Envelopes on Trees; Heldermann Verlag; Journal Of Convex Analysis; 27; 4; 11-2020; 1195-1218
0944-6532
CONICET Digital
CONICET
Autor
del Pezzo, Leandro Martin
Frevenza Maestrone, Nicolas Federico
Rossi, Julio Daniel
Resumen
We introduce two notions of convexity for an infinite regular tree. For these two notions we show that given a continuous boundary datum there exists a unique convex envelope on the tree and characterize the equation that this envelope satisfies. We also relate the equation with two versions of the Laplacian on the tree. Moreover, for a function defined on the tree, the convex envelope turns out to be the solution to the obstacle problem for this equation.