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We consider second-order divergence form uniformly parabolic and ellipticPDEs with bounded and $VMO_{x}$ leading coefficients and possibly linearlygrowing lower-order coefficients. We look for solutions which are summable tothe $p$th power with respect to the usual Lebesgue measure along with theirfirst derivatives with respect to the spatial variables.

On divergence form second-order PDEs with growing coefficients in $W^{1}_{p}$ spaces without weights