Differential and Integral Equations

A boundary estimate for nonlinear equations with discontinuous coefficients

Juha Kinnunen and Shulin Zhou

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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

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

First available in Project Euclid: 21 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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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