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On the Cauchy Problem for Integro-Differential Equations in the Scale of Spaces of Generalized Smoothness

  • R. Mikulevičius
  • C. Phonsom
Article

Abstract

Parabolic integro-differential model Cauchy problem is considered in the scale of L p -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.

Keywords

Non-local parabolic integro-differential equations Lévy processes 

Mathematics Subject Classification (2010)

35R09 60J75 35B65 

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Notes

Acknowledgments

We are very grateful to our reviewers for valuable comments and suggestions.

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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of Southern CaliforniaLos AngelesUSA

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