Weighted estimates for nonhomogeneous quasilinear equations with discontinuous coefficients
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 10 (2011) no. 1, p. 1-17

We obtain local and global ${W}^{1,\phantom{\rule{0.166667em}{0ex}}q}$ estimates on weighted Lebesgue spaces with certain Muckenhoupt weights for solutions to a nonhomogeneous $p$-Laplace type equation with $VMO$ coefficients in a ${𝒞}^{1}$ domain. These estimates can be viewed as weighted norm inequalities for certain nonlinear singular operators (without any explicit kernel) arising from the $p$-Laplacian, and are applicable to a quasilinear Riccati type equation.

Published online : 2018-06-21
Classification:  35R05,  35J92,  42B37,  35J15,  35J25,  42B25,  42B99
@article{ASNSP_2011_5_10_1_1_0,
author = {Nguyen, Cong Phuc},
title = {Weighted estimates for nonhomogeneous quasilinear equations with discontinuous coefficients},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 10},
number = {1},
year = {2011},
pages = {1-17},
zbl = {1228.35260},
mrnumber = {2829320},
language = {en},
url = {http://www.numdam.org/item/ASNSP_2011_5_10_1_1_0}
}

Nguyen, Cong Phuc. Weighted estimates for nonhomogeneous quasilinear equations with discontinuous coefficients. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 10 (2011) no. 1, pp. 1-17. http://www.numdam.org/item/ASNSP_2011_5_10_1_1_0/

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