On the Cauchy problem for nondegenerate parabolic integro-differential equations in the scale of generalized H\"older spaces

TL;DR

This paper investigates the existence, uniqueness, and estimates of solutions for nondegenerate parabolic integro-differential equations within generalized Hölder spaces defined by radially O-regularly varying Lévy measures.

Contribution

It introduces a framework for analyzing such equations in a generalized Hölder space setting based on specific Lévy measures, extending previous regularity results.

Findings

Proved existence and uniqueness of solutions.

Derived a priori estimates for solutions.

Established regularity results in generalized Hölder spaces.

Abstract

Parabolic integro-differential non degenerate Cauchy problem is considered in the scale of H\"older spaces of functions whose regularity is defined by a radially O-regularly varying L\'evy measure. Existence and uniqueness and the estimates of the solution are derived.