Open Access
January/February 2012 Boundedness of weak solutions of degenerate quasilinear equations with rough coefficients
D.D. Monticelli, S. Rodney, R.L. Wheeden
Differential Integral Equations 25(1/2): 143-200 (January/February 2012). DOI: 10.57262/die/1356012830


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.


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D.D. Monticelli. S. Rodney. R.L. Wheeden. "Boundedness of weak solutions of degenerate quasilinear equations with rough coefficients." Differential Integral Equations 25 (1/2) 143 - 200, January/February 2012.


Published: January/February 2012
First available in Project Euclid: 20 December 2012

zbMATH: 1249.35117
MathSciNet: MR2906551
Digital Object Identifier: 10.57262/die/1356012830

Primary: 35B65 , 35J60 , 35J70

Rights: Copyright © 2012 Khayyam Publishing, Inc.

Vol.25 • No. 1/2 • January/February 2012
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