On the Cauchy Problem for Integro-Differential Equations in the Scale of Spaces of Generalized Smoothness
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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.
KeywordsNon-local parabolic integro-differential equations Lévy processes
Mathematics Subject Classification (2010)35R09 60J75 35B65
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We are very grateful to our reviewers for valuable comments and suggestions.
- 3.Garcia-Cuerva, J., Rubio De Francia, J.L.: Weighted Norm Inequalities and Related Topics. North-Holland (1985)Google Scholar
- 4.Farkas, W., Jacob, N., Schilling, R. L.: Function spaces related to continuous negative definite functions: ψ -Bessel potential spaces. Diss. Math., 1–60 (2001)Google Scholar
- 10.Kim, I., Kim, K. -H.: An L p,-boundedness of stochastic singular integral operators and its application to SPDEs, arXiv:1608.08728 (2016)
- 12.Stein, E.: Harmonic Analysis. Princeton University Press (1993)Google Scholar
- 13.Triebel, H.: Interpolation Theory, Function Spaces. Differential Operators. North-Holland (1978)Google Scholar