Differential and Integral Equations

Boundedness of weak solutions of degenerate quasilinear equations with rough coefficients

D.D. Monticelli, S. Rodney, and R.L. Wheeden

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We derive local boundedness estimates for weak solutions of a large class of second-order quasilinear equations. The structural assumptions imposed on an equation in the class allow vanishing of the quadratic form associated with its principal part and require no smoothness of its coefficients. The class includes second-order linear elliptic equations as studied in [5] and second-order subelliptic linear equations as in [8, 9]. Our results also extend ones obtained by J. Serrin [7] concerning local boundedness of weak solutions of quasilinear elliptic equations.

Article information

Differential Integral Equations, Volume 25, Number 1/2 (2012), 143-200.

First available in Project Euclid: 20 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J70: Degenerate elliptic equations 35J60: Nonlinear elliptic equations 35B65: Smoothness and regularity of solutions


Monticelli, D.D.; Rodney, S.; Wheeden, R.L. Boundedness of weak solutions of degenerate quasilinear equations with rough coefficients. Differential Integral Equations 25 (2012), no. 1/2, 143--200. https://projecteuclid.org/euclid.die/1356012830

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