JournalszaaVol. 28 , No. 2DOI 10.4171/zaa/1377

<em>W<sup>2,p</sup></em>- and <em>W<sup>1,p</sup></em>-Estimates at the Boundary for Solutions of Fully Nonlinear, Uniformly Elliptic Equations

  • Niki Winter

    RWTH Aachen, Germany
<em>W<sup>2,p</sup></em>- and <em>W<sup>1,p</sup></em>-Estimates at the Boundary for Solutions of Fully Nonlinear, Uniformly Elliptic Equations cover

Abstract

In this paper we extend Caffarelli's result on interior W2,pW^{2,p}-estimates for viscosity solutions of uniformly elliptic equations and prove W2,pW^{2,p}-estimates at a flat boundary. Moreover we extend a result of A.~\'Swiech and prove W1,pW^{1,p}-estimates at the boundary. Thereafter we combine these results and prove global W2,pW^{2,p}-estimates for equations with dependence on DuDu and uu. Finally, we show that the previous estimates lead to an existence result for W2,pW^{2,p}-strong solutions.}