Abstract
We establish optimal gradient estimates in Orlicz space for a nonhomogeneous elliptic equation of higher order with discontinuous coefficients on a nonsmooth domain. Our assumption is that for each point and for each sufficiently small scale the coefficients have small mean oscillation and the boundary of the domain is sufficiently close to a hyperplane. As a consequence we prove the classical Wm,p, m=1,2,..., 1<p<∞, estimates for such a higher order equation. Our results easily extend to higher order elliptic and parabolic systems.
Original language | English |
---|---|
Pages (from-to) | 243-263 |
Number of pages | 21 |
Journal | Journal of Differential Equations |
Volume | 250 |
Issue number | 1 |
DOIs | |
State | Published - 1 Jan 2011 |
Keywords
- BMO space
- Gradient estimate
- Higher order equation
- Orlicz space
- Primary
- Reifenberg domain
- Reverse Hölder inequality
- Secondary