Applied Mathematics and Optimization

, Volume 9, Issue 1, pp 177-191

First online:

Integro-differential operators associated with diffusion processes with jumps

  • Suzanne LenhartAffiliated withDepartment of Mathematics, University of Tennessee

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We show existence andW loc 2,p ⋂ W1,∞-regularity results for the integro-differential equation, associated with a diffusion process with jumps on a bounded domain. The second order elliptic partial differential operator and the integral operator involved here are both maximum principle type operators, which enables us to makeW 1,∞ a priori estimates.