Abstract
We prove mixed Lp(Lq)-estimates, with p,q∈(1,∞), for higher-order elliptic and parabolic equations on the half space R+ d+1 with general boundary conditions which satisfy the Lopatinskii–Shapiro condition. We assume that the elliptic operators A have leading coefficients which are in the class of vanishing mean oscillations both in the time variable and the space variable. In the proof, we apply and extend the techniques developed by Krylov [24] as well as Dong and Kim in [13] to produce mean oscillation estimates for equations on the half space with general boundary conditions.
Original language | English |
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Pages (from-to) | 1993-2038 |
Number of pages | 46 |
Journal | Journal of Functional Analysis |
Volume | 274 |
Issue number | 7 |
DOIs | |
Publication status | Published - 2018 |
Keywords
- Inhomogeneous boundary conditions
- Mixed-norms
- Muckenhoupt weights
- The Lopatinskii–Shapiro condition