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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Abstract

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

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

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356012830

Mathematical Reviews number (MathSciNet)
MR2906551

Zentralblatt MATH identifier
1249.35117

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

Citation

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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