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Parabolic equations with variably partially VMO coefficients

146   0   0.0 ( 0 )
 نشر من قبل Hongjie Dong
 تاريخ النشر 2008
  مجال البحث
والبحث باللغة English
 تأليف Hongjie Dong




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We prove the $W^{1,2}_{p}$-solvability of second order parabolic equations in nondivergence form in the whole space for $pin (1,infty)$. The leading coefficients are assumed to be measurable in one spatial direction and have vanishing mean oscillation (VMO) in the orthogonal directions and the time variable in each small parabolic cylinder with the direction depending on the cylinder. This extends a recent result by Krylov [17] for elliptic equations and removes the restriction that $p>2$.



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