Higher-Order Parabolic Equations with VMO Assumptions and General Boundary Conditions with Variable Leading Coefficients
2018 ◽
Vol 2020
(7)
◽
pp. 2114-2144
◽
Keyword(s):
Abstract We prove weighted mixed $L_{p}(L_{q})$-estimates, with $p,q\in (1,\infty )$, and the corresponding solvability results for higher-order elliptic and parabolic equations on the half space ${\mathbb{R}}^{d+1}_{+}$ and on general $C^{2m-1,1}$ domains with general boundary conditions, which satisfy the Lopatinskii–Shapiro condition. We assume that the elliptic operators A have leading coefficients that are in the class of vanishing mean oscillations both in the time and the space variables and that the boundary operators have variable leading coefficients. The proofs are based on and generalize the estimates recently obtained by the authors in [6].
2018 ◽
Vol 274
(7)
◽
pp. 1993-2038
◽
Keyword(s):
2019 ◽
Vol 33
(5)
◽
pp. 2289-2305
◽
Keyword(s):
Keyword(s):
2017 ◽
Vol 108
◽
pp. 75-90
◽
Keyword(s):
1980 ◽
Vol 259
(1)
◽
pp. 299-299
◽