TY - JOUR
AU1 - Zhang, Junjie
AU2 - Zheng, Shenzhou
AB - In this paper, we mainly prove a local Calderón–Zygmund estimate in the Lorentz spaces with a variable power 
$$p(\cdot )$$



p
(
·
)



 to the Hessian of nondivergence parabolic equations 
$$u_{t}(x,t)-a_{ij}(x,t)D_{ij}u(x,t)=f(x,t)$$




u
t


(
x
,
t
)

-

a

ij



(
x
,
t
)


D

ij


u

(
x
,
t
)

=
f

(
x
,
t
)




, under assumptions that the variable exponent 
$$p(\cdot )$$



p
(
·
)



 is 
$$\log $$


log


-Hölder continuous, and the coefficient is a small partially BMO matrix which means that 
$$a_{ij}(x,t)$$




a

ij



(
x
,
t
)




 is merely measurable in one of spatial variables and have small BMO semi-norms with respect to other variables. In addition, we also derive a similar result for nondivergence elliptic equations 
$$a_{ij}(x)D_{ij}u(x)=f(x)$$




a

ij



(
x
)


D

ij


u

(
x
)

=
f

(
x
)




 with small partially BMO coefficients.
TI - Hessian Estimates for Nondivergence Parabolic and Elliptic Equations with Partially BMO Coefficients
JF - Results in Mathematics
DO - 10.1007/s00025-019-1147-z
DA - 2019-12-27
UR - https://www.deepdyve.com/lp/springer-journals/hessian-estimates-for-nondivergence-parabolic-and-elliptic-equations-3ANCLzHOzY
SP - 1
EP - 31
VL - 75
IS - 1
DP - DeepDyve
ER -