| Abstract: |
| We study a very general quasilinear elliptic equation with the
nonlinearity with Orlicz growth subject to a degenerate or singular
matrix-valued weight on a bounded nonsmooth domain. The nonlinearity
satisfies a nonstandard growth condition related to the associated
Young function, and the logarithm of the matrix-valued weight in BMO
is constrained by a smallness parameter which has a close
relationship with the Young function. We establish a global
Calder\`{o}n-Zygmund estimate for the weak solution of such a
degenerate or singular problem in the setting of a weighted Orlicz
space under a minimal geometric assumption that the boundary of the
domain is sufficiently flat in the Reifenberg sense. |
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