Integro-differential equations with L{é}vy operators for degenerate jumps depending on spaces and gradients

Mathematics – Analysis of PDEs

Scientific paper

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Submitted in May 2011, to JMPA

Scientific paper

We establish the comparison principle and the existence of solutions of the
integro-differential equations with L{\'e}vy operators. The L{\'e}vy operators
of our interest are infinitesmal generator of the jump processes which could be
degenerate and may depend on the gradient of the solutions.

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