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Keywords:
nonstandard growth; $C^{1, \alpha }$ regularity; Hölder continuity; bounded weak solution; partial differential equations
Summary:
We study elliptic equations with the general nonstandard growth conditions involving Lebesgue measurable functions on $\Omega $. We prove the global $C^{1, \alpha }$ regularity of bounded weak solutions of these equations with the Dirichlet boundary condition. Our results generalize the $C^{1, \alpha }$ regularity results for the elliptic equations in divergence form not only in the variable exponent case but also in the constant exponent case.
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