Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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GLOBAL GRADIENT ESTIMATES FOR NONLINEAR ELLIPTIC EQUATIONS

  • Received : 2014.02.14
  • Published : 2014.11.01
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Abstract

We prove global gradient estimates in weighted Orlicz spaces for weak solutions of nonlinear elliptic equations in divergence form over a bounded non-smooth domain as a generalization of Calder$\acute{o}$n-Zygmund theory. For each point and each small scale, the main assumptions are that nonlinearity is assumed to have a uniformly small mean oscillation and that the boundary of the domain is sufficiently flat.

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References

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  1. Weighed Estimates for Nonlinear Elliptic Problems with Orlicz Data vol.1, pp.1, 2015, https://doi.org/10.1007/BF03377367