JournalsaihpcVol. 30, No. 2pp. 291–313

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

  • Sun-Sig Byun

    Department of Mathematics and Research Institute of Mathematics, Seoul National University, Seoul 151-747, Republic of Korea
  • Seungjin Ryu

    Department of Mathematics, Seoul National University, Seoul 151-747, Republic of Korea
Global weighted estimates for the gradient of solutions to nonlinear elliptic equations cover
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Abstract

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 LqL^{q} estimates with q(p,)q \in (p,\infty ) for the gradient of weak solutions.

Cite this article

Sun-Sig Byun, Seungjin Ryu, Global weighted estimates for the gradient of solutions to nonlinear elliptic equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 30 (2013), no. 2, pp. 291–313

DOI 10.1016/J.ANIHPC.2012.08.001