Differential and Integral Equations

A boundary estimate for nonlinear equations with discontinuous coefficients

Juha Kinnunen and Shulin Zhou

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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

Subjects
Primary: 35J60: Nonlinear elliptic equations
Secondary: 35B45: A priori estimates 35B65: Smoothness and regularity of solutions

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


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