On L_p- theory for integro-differential operators with spatially dependent coefficients

2023/08/30 by Sutawas Janreung, Janreung, Sutawas, Tatpon Siripraparat +3
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2308.16127

openalex publication_date 2023/08/30 · openalex created_date 2023/09/02 · openalex updated_date 2026/07/28

Abstract

The parabolic integro-differential Cauchy problem with spatially dependent coefficients is considered in generalized Bessel potential spaces where smoothness is defined by Lévy measures with O-regularly varying profile. The coefficients are assumed to be bounded and Hölder continuous in the spatial variable. Our results can cover interesting classes of Lévy measures that go beyond those comparable to dy/|y|^d+α.

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