Integro-differential equations with Lévy operators for degenerate jumps depending on spaces and gradients

2010/12/14 by Mariko Arisawa, M. Arisawa, Arisawa, M.
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Probability (math.PR) #Stability and Controllability of Differential Equations #math.AP #math.PR

paper · pdf · doi:10.48550/arxiv.1012.3069

Submitted in May 2011, to JMPA

openalex publication_date 2010/12/14 · arxiv created 2011/10/07 · arxiv updated 2011/10/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We establish the comparison principle and the existence of solutions of the integro-differential equations with Lévy operators. The Lévy 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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