- and -Estimates at the Boundary for Solutions of Fully Nonlinear, Uniformly Elliptic Equations

  • Niki Winter

    RWTH Aachen, Germany

Abstract

In this paper we extend Caffarelli's result on interior -estimates for viscosity solutions of uniformly elliptic equations and prove -estimates at a flat boundary. Moreover we extend a result of A.~\'Swiech and prove -estimates at the boundary. Thereafter we combine these results and prove global -estimates for equations with dependence on and . Finally, we show that the previous estimates lead to an existence result for -strong solutions.}

Cite this article

Niki Winter, - and -Estimates at the Boundary for Solutions of Fully Nonlinear, Uniformly Elliptic Equations. Z. Anal. Anwend. 28 (2009), no. 2, pp. 129–164

DOI 10.4171/ZAA/1377