Asymptotic Mean-Value Formulas for Solutions of General Second-Order Elliptic Equations

TL;DR

This paper develops asymptotic mean-value formulas for solutions to a broad class of second-order elliptic equations, including well-known operators like Pucci, Issacs, and k-Hessian, using a flexible approach.

Contribution

It introduces a versatile method to derive mean-value formulas for various elliptic operators, extending classical results to more complex and combined operator families.

Findings

Derived asymptotic mean-value formulas for multiple elliptic operators.

Unified approach applicable to infimum, supremum, and combined operator families.

Includes classical operators such as Pucci, Issacs, and k-Hessian as special cases.

Abstract

We obtain asymptotic mean-value formulas for solutions of second-order elliptic equations. Our approach is very flexible and allows us to consider several families of operators obtained as an infimum, a supremum, or a combination of both infimum and supremum, of linear operators. The families of equations that we consider include well-known operators such as Pucci, Issacs, and $k$-Hessian operators.