Representation formula for viscosity solution to a PDE problem involving Pucci’s extremal operator. (English) Zbl 1454.35049
Summary: We provide a representation formula for viscosity solutions to an elliptic Dirichlet problem involving Pucci’s extremal operators. This is done through a dynamic programming principle derived from [L. Denis et al., Potential Anal. 34, No. 2, 139–161 (2011; Zbl 1225.60057)]. The formula can be seen as a nonlinear extension of the Feynman-Kac formula.
MSC:
| 35D40 | Viscosity solutions to PDEs |
| 35C15 | Integral representations of solutions to PDEs |
| 35J25 | Boundary value problems for second-order elliptic equations |
Keywords:
nonlinear Feynman-Kac formula; Pucci’s extremal operators; dynamic programming principle; elliptic Dirichlet problemCitations:
Zbl 1225.60057References:
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