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

2016/05/23 by R. Mikulevíčius, R. Mikulevicius, Mikulevicius, R. +2
Economics, Econometrics and Finance · Mathematics · #35B65 #45K05 #60J75 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #advanced mathematical theories #math.AP #math.PR #msc:35B65 #msc:45K05 #msc:60J75

paper · pdf · doi:10.48550/arxiv.1605.07086

arxiv created 2016/05/23 · openalex publication_date 2016/05/23 · arxiv updated 2016/05/24 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Elliptic and parabolic integro-differential model problems are considered in the whole space. By verifying Hörmander 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.

Cited by

• A regularity theory for evolution equations with space-time anisotropic non-local operators in mixed-norm Sobolev spaces

Related

• On the Cauchy problem for integro-differential equations in the scale of spaces of generalized smoothness
• On the Cauchy problem for stochastic integrodifferential parabolic equations in the scale of Lp-spaces of generalized smoothness
• On L_p- theory for integro-differential operators with spatially dependent coefficients
• On the Cauchy problem for parabolic integro-differential equations in generalized Hölder spaces
• L^p-maximal regularity of nonlocal parabolic equation and applications