## Differential and Integral Equations

### A boundary estimate for nonlinear equations with discontinuous coefficients

#### Abstract

We prove a boundary estimate for the gradient of a weak solution to a partial differential equation of $p$-Laplacian type with coefficients of vanishing mean oscillation. Combining the boundary estimate with a known interior estimate we obtain a global higher integrability result. The main result generalizes known results for linear equations to a nonlinear case. Our method is based on choosing the right test function, and, in particular, we do not use any representation formulas for solutions.

#### Article information

Source
Differential Integral Equations, Volume 14, Number 4 (2001), 475-492.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356123316

Mathematical Reviews number (MathSciNet)
MR1799417

Zentralblatt MATH identifier
1161.35394

#### Citation

Kinnunen, Juha; Zhou, Shulin. A boundary estimate for nonlinear equations with discontinuous coefficients. Differential Integral Equations 14 (2001), no. 4, 475--492. https://projecteuclid.org/euclid.die/1356123316