Consider
![Rendered by QuickLaTeX.com \[\left(a^{11}+a^{22}\right)u_t - \sum_{i,j=1}^2 a^{ij}(t,x_1,x_2) D_{ij}u = f,\]](https://mathematicians.korea.ac.kr/dkim/wp-content/ql-cache/quicklatex.com-cf566bc2d4ccbdeded391534b113dadd_l3.png)
where
are measurable in
and
is measurable in
, but constant in
.
Set
![]()
We use the inequality
![]()
Parabolic equations with measurable coefficients in $\mathbb{R} \times \mathbb{R}^2$
Consider
![Rendered by QuickLaTeX.com \[\left(a^{11}+a^{22}\right)u_t - \sum_{i,j=1}^2 a^{ij}(t,x_1,x_2) D_{ij}u = f,\]](https://mathematicians.korea.ac.kr/dkim/wp-content/ql-cache/quicklatex.com-cf566bc2d4ccbdeded391534b113dadd_l3.png)
where
are measurable in
and
is measurable in
, but constant in
.
Set
![]()
We use the inequality
![]()