Asymptotic mean-value formulas for solutions of general second-order elliptic equations

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.

Keywords

• mean-value formulas
• viscosity solutions
• k-hessian equation
• issacs equation
• 35j60
• 35d40
• 35b05