Colloquium

Speaker: | Prof. Ki-Ahm Lee (Seoul National University) |

Title: | Regularity theory for fully nonlinear integro-differential operators |

Time: | 2011-10-06 (Thu.) 15:00 - 16:00 |

Place: | Auditorium, 6 Floor, Institute of Mathematics (NTU Campus) |

Abstract: | In this talk, we are going to consider the regularity of the viscosity solutions of integro-dierential operators with possibly nonsymmetric kernel: $Lu(x) = p.v.\int_{R^n}\mu (u;x;y)K(y)\, dy$ where $\mu (u;x; y) = u(x+y)-u(x)-(\nabla u(x)\cdot y)\chi_{B_1}(y)$, which describes the infinitesimal generator of given purely jump processes, i.e. processes without diffusion or drift part And fully nonlinear integro-dierential equations come from the stochastic control theory related with $\mathcal{I}u(x) = sup_{\alpha}\mathcal{L}_{\alpha} u(x)$ or game theory associated with $\mathcal{I}u(x) = inf_{\beta}sup_{\alpha}\mathcal{L}_{\alpha\beta} u(x)$ when the stochastic process is of Levy type allowing jumps. We are are going to discuss recent results on estimates and asymptotic analysis. |

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