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This paper is to prove global regularity estimates for solutions to the second-order elliptic equation in non-divergence form with BMO coefficients in a C1,1 domain on weighted variable exponent Lebesgue spaces. Our approach is based on the representations for the solutions to the non-divergence elliptic equations and the domination technique by sparse operators in harmonic analysis.
- Non-divergence elliptic equation
- weighted variable exponent Lebesgue space
- bounded mean oscillation (BMO) space
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