info:eu-repo/semantics/article
Tug-of-War games and parabolic problems with spatial and time dependence
Fecha
2014Registro en:
del Pezzo, Leandro Martin; Rossi, Julio Daniel; Tug-of-War games and parabolic problems with spatial and time dependence; Khayyam Publishing; Differential and Integral Equations; 27; 3-4; 2014; 269-288
0893-4983
CONICET Digital
CONICET
Autor
del Pezzo, Leandro Martin
Rossi, Julio Daniel
Resumen
In this paper we use probabilistic arguments (Tug-of-War games) to obtain existence of viscosity solutions to a parabolic problem of the form {K(x,t)(Du)ut(x,t)=12⟨D2uJ(x,t)(Du),J(x,t)(Du)(x,t)⟩u(x,t)=F(x)in ΩT,on Γ, where ΩT=Ω×(0,T]ΩT=Ω×(0,T] and ΓΓ is its parabolic boundary. This problem can be viewed as a version with spatial and time dependence of the evolution problem given by the infinity Laplacian, ut(x,t)=⟨D2u(x,t)Du|Du|(x,t),Du|Du|(x,t)⟩.