Parabolic and elliptic systems in divergence form with variably partially BMO coefficients

Abstract

We establish the solvability of second order divergence type parabolic systems in Sobolev spaces. The leading coefficients are assumed to be only measurable in one spatial direction on each small parabolic cylinder with the spatial direction allowed to depend on the cylinder. In the other orthogonal directions and the time variable the coefficients have locally small mean oscillations. We also obtain the corresponding $W_p^1$-solvability of second order elliptic systems in divergence form. Our results are new even for scalar equations and the proofs simplify the methods used previously in [12]

minor revision with an application to elasticity systems, 23 pages, to appear in SIAM J. Math. Anal

References in corpus (4)

• Elliptic equations in divergence form with partially BMO coefficients
• A'priori estimates and precise regularity for parabolic systems with discontinuous data
• Global regularity of weak solutions to quasilinear elliptic and parabolic equations with controlled growth
• Parabolic equations with variably partially VMO coefficients

Cited by in corpus (1)

• A weighted $L_p$-theory for parabolic PDEs with BMO coefficients on $C^1$-domains