### $W^1,p$-interior estimates for solutions of fully nonlinear, uniformly elliptic equations

Andrzej Świech

#### Abstract

We prove $W^{1,p}$-interior estimates for viscosity solutions of fully nonlinear, uniformly elliptic equations. The estimates complement $C^{1,\alpha}$-regularity results of L. Caffarelli. We apply the estimates to obtain existence and uniqueness of viscosity and strong solutions of Dirichlet boundary value problems.

#### Article information

Source
Adv. Differential Equations, Volume 2, Number 6 (1997), 1005-1027.

Dates
First available in Project Euclid: 22 April 2013

Świech, Andrzej. $W^1,p$-interior estimates for solutions of fully nonlinear, uniformly elliptic equations. Adv. Differential Equations 2 (1997), no. 6, 1005--1027. https://projecteuclid.org/euclid.ade/1366638681