Advances in Differential Equations

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

Andrzej Świech

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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

Permanent link to this document
https://projecteuclid.org/euclid.ade/1366638681

Mathematical Reviews number (MathSciNet)
MR1606359

Zentralblatt MATH identifier
1023.35509

Subjects
Primary: 35J65: Nonlinear boundary value problems for linear elliptic equations
Secondary: 35B45: A priori estimates 35B65: Smoothness and regularity of solutions 49L25: Viscosity solutions

Citation

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.


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