Differential and Integral Equations

Tug-of-War games and parabolic problems with spatial and time dependence

Leandro M. Del Pezzo and Julio D. Rossi

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

In this paper, we use probabilistic arguments (Tug-of-War games) to obtain the existence of viscosity solutions to a parabolic problem of the form $$ \begin{cases} K_{(x,t)}(D u )u_t (x,t)= \tfrac12 \langle D^2 u J_{(x,t)}(D u ),J_{(x,t)}(D u) (x,t)\rangle & \mbox{in } \Omega_T,\\ u(x,t)=F(x) & \mbox{on }\Gamma, \end{cases} $$ where $\Omega_T=\Omega\times(0,T]$ and $\Gamma$ 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, $$ u_t (x,t)= \langle D^2 u (x,t) \frac{D u}{|Du|} (x,t),\, \frac{D u}{|Du|} (x,t)\rangle\, . $$

Article information

Source
Differential Integral Equations, Volume 27, Number 3/4 (2014), 269-288.

Dates
First available in Project Euclid: 30 January 2014

Permanent link to this document
https://projecteuclid.org/euclid.die/1391091366

Mathematical Reviews number (MathSciNet)
MR3161604

Zentralblatt MATH identifier
1324.35065

Subjects
Primary: 35B05: Oscillation, zeros of solutions, mean value theorems, etc. 35J25: Boundary value problems for second-order elliptic equations 35J69

Citation

Del Pezzo, Leandro M.; Rossi, Julio D. Tug-of-War games and parabolic problems with spatial and time dependence. Differential Integral Equations 27 (2014), no. 3/4, 269--288. https://projecteuclid.org/euclid.die/1391091366


Export citation