info:eu-repo/semantics/article
A limiting free boundary problem with gradient constraint and Tug-of-War games
Fecha
2019-01Registro en:
Blanc, Pablo; Da Silva, Joao Vitor; Rossi, Julio Daniel; A limiting free boundary problem with gradient constraint and Tug-of-War games; Springer Heidelberg; Annali Di Matematica Pura Ed Applicata; 198; 1-2019; 1441-1469
0373-3114
CONICET Digital
CONICET
Autor
Blanc, Pablo
Da Silva, Joao Vitor
Rossi, Julio Daniel
Resumen
In this manuscript we deal with regularity issues and the asymptotic behaviour (as p → ∞) of solutions for elliptic free boundary problems of p−Laplacian type (2 ≤ p < ∞): −pu(x) + λ0(x)χ{u>0}(x) = 0 in ⊂ RN , with a prescribed Dirichlet boundary data, where λ0 > 0 is a bounded function and is a regular domain. First, we prove the convergence as p → ∞ of any family of solutions (u p)p≥2, as well as we obtain the corresponding limit operator (in non-divergence form) ruling the limit equation, max −∞u∞, −|∇u∞| + χ{u∞>0} = 0 in ∩ {u∞ ≥ 0} u∞ = F on ∂ . Next, we obtain uniqueness for solutions to this limit problem. Finally, we show that any solution to the limit operator is a limit of value functions for a specific Tug-of-War game.