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

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

2009-09-29

arxiv.org/abs/0909.5248v1

Mathematics

Analysis of PDEs

25 pages

Scientific paper

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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