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arXiv · 1705.09256

On the Cauchy problem for integro-differential equations in the scale of spaces of generalized smoothness

R. Mikulevicius·C. Phonsom
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Abstract

Parabolic integro-differential model Cauchy problem is considered in the scale of Lp -spaces of functions whose regularity is defined by a scalable Levy measure. Existence and uniqueness of a solution is proved by deriving apriori estimates. Some rough probability density function estimates of the associated Levy process are used as well.

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R. Mikulevicius, C. Phonsom. 2017-05-25. On the Cauchy problem for integro-differential equations in the scale of spaces of generalized smoothness. https://arxiv.org/abs/1705.09256

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