Weighted estimates for nonhomogeneous quasilinear equations with discontinuous coefficients

Nguyen, Cong Phuc

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 10 (2011) no. 1, pp. 1-17.

We obtain local and global $W^{1,q}$ 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.

Classification : 35R05, 35J92, 42B37, 35J15, 35J25, 42B25, 42B99

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