arXiv:1605.07086 Abstract | arXiv Analytics

arXiv:1605.07086 [math.AP]Abstract References Reviews Resources

On Lp -theory for parabolic and elliptic integro-differential equations with scalable operators in the whole space

Published 2016-05-23Version 1

Elliptic and parabolic integro-differential model problems are considered in the whole space. By verifying H\"ormander condition, the existence and uniqueness is proved in L_{p}-spaces of functions whose regularity is defined by a scalable, possibly nonsymmetric, Levy measure. Some rough probability density function estimates of the associated Levy process are used as well.

Categories: math.AP, math.PR

Subjects: 45K05, 60J75, 35B65

Keywords: elliptic integro-differential equations, scalable operators, rough probability density function estimates, parabolic integro-differential model problems

Related articles:

arXiv:1805.03232 [math.AP] (Published 2018-05-08)

On the Cauchy problem for stochastic integrodifferential parabolic equations in the scale of Lp-spaces of generalized smoothness

R. Mikulevicius, C. Phonsom

arXiv:2205.05531 [math.AP] (Published 2022-05-11)

Nonlocal operators related to nonsymmetric forms II: Harnack inequalities

Moritz Kassmann, Marvin Weidner

arXiv:1805.09688 [math.AP] (Published 2018-05-23)

A Hamilton-Jacobi method to describe the evolutionary equilibria in heterogeneous environments and with non-vanishing effects of mutations