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

N. V. Krylov

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arXiv · 0909.5248

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

N. V. Krylov

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Abstract

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

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N. V. Krylov. 2009-09-29. On divergence form second-order PDEs with growing coefficients in $W^{1}_{p}$ spaces without weights. https://arxiv.org/abs/0909.5248

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