Global weighted estimates for the gradient of solutions to nonlinear elliptic equations

Byun, Sun-Sig; Ryu, Seungjin

Annales de l'I.H.P. Analyse non linéaire, Tome 30 (2013) no. 2, pp. 291-313.

We consider nonlinear elliptic equations of p-Laplacian type that are not necessarily of variation form when the nonlinearity is allowed to be discontinuous and the boundary of the domain can go beyond the Lipschitz category. Under smallness in the BMO nonlinearity and sufficient flatness of the Reifenberg domain, we obtain the global weighted $L^q$ estimates with $q\in (p,\infty )$ for the gradient of weak solutions.

Classification : 35J60, 35R05, 46E30, 46E35
Mots clés : Gradient estimate, Weighted $ {L}^{p}$ space, Nonlinear elliptic equation, BMO space, Reifenberg domain

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