Rang, Marcus: Regularity results for nonlocal fully nonlinear elliptic equations. 2013
Inhalt
- Introduction
- Motivation
- Known Regularity Results for Fully Nonlinear Integro-Differential Equations
- Setting and Outline
- Notation
- Regularity Estimates for Local Fully Nonlinear Elliptic Equations
- Viscosity Solutions
- The Class S of Solutions to Special Types of Uniformly Elliptic Equations
- Aleksandrov-Bakelman-Pucci Estimate
- Harnack Inequality and Hölder Regularity for Viscosity Solutions and the class S
- Regularity Estimates for Nonlocal Fully Nonlinear Elliptic Equations
- Motivation and Basic Definitions
- A special Class of Operators
- Existence of Solutions to the Nonlocal Dirichlet Problem
- A nonlocal Aleksandrov-Bakelman-Pucci Estimate
- Bump Functions
- Point Estimates
- Hölder Regularity
- C Regularity
- Conclusion
- Bibliography