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March/April 2014 Tug-of-War games and parabolic problems with spatial and time dependence
Leandro M. Del Pezzo, Julio D. Rossi
Differential Integral Equations 27(3/4): 269-288 (March/April 2014).

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, $$ u_t (x,t)= \langle D^2 u (x,t) \frac{D u}{|Du|} (x,t),\, \frac{D u}{|Du|} (x,t)\rangle\, . $$

Citation

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Leandro M. Del Pezzo. Julio D. Rossi. "Tug-of-War games and parabolic problems with spatial and time dependence." Differential Integral Equations 27 (3/4) 269 - 288, March/April 2014.

Information

Published: March/April 2014
First available in Project Euclid: 30 January 2014

zbMATH: 1324.35065
MathSciNet: MR3161604

Subjects:
Primary: 35B05, 35J25, 35J69

Rights: Copyright © 2014 Khayyam Publishing, Inc.

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Vol.27 • No. 3/4 • March/April 2014
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