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Chaker, Jamil: Analysis of anisotropic nonlocal operators and jump processes. 2017
Inhalt
Introduction
Outline
Notation
Basics
Analytic Basics
Lebesgue spaces
Lorentz spaces
Sobolev spaces
John-Nirenberg's lemma for doubling measures
Probabilistic Basics
Preliminaries
Lévy Processes
Stochastic calculus
Systems of stochastic differential equations
Preliminaries
Existence
Uniqueness
Perturbation
Boundedness of the Resolvent
Auxiliary results
Proof of the uniqueness for solutions to the system of stochastic differential equations
Regularity estimates for anisotropic nonlocal equations
Nonlocal equations and weak solutions
An algebraic inequality
Some technical observations
Proof of the inequality
Properties of weak supersolutions
The weak Harnack inequality
Hölder regularity for weak solutions
Examples
Bibliography