Parabolic and elliptic equations with VMO coefficients

Research paper by N. V. Krylov

Indexed on: 30 Nov '05Published on: 30 Nov '05Published in: Mathematics - Analysis of PDEs


An $L_{p}$-theory of divergence and non-divergence form elliptic and parabolic equations is presented. The main coefficients are supposed to belong to the class $VMO_{x}$, which, in particular, contains all functions independent of $x$. Weak uniqueness of the martingale problem associated with such equations is obtained.