Differential and Integral Equations
- Differential Integral Equations
- Volume 25, Number 1/2 (2012), 143-200.
Boundedness of weak solutions of degenerate quasilinear equations with rough coefficients
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  and second-order subelliptic linear equations as in [8, 9]. Our results also extend ones obtained by J. Serrin  concerning local boundedness of weak solutions of quasilinear elliptic equations.
Differential Integral Equations, Volume 25, Number 1/2 (2012), 143-200.
First available in Project Euclid: 20 December 2012
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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