We prove the existence and uniqueness of solutions in Sobolev spaces to second-order parabolic equations in non-divergence form. The coefficients (except one of them) of second-order terms of the equations are measurable in both time and one spatial variables, and VMO (vanishing mean oscillation) in other spatial variables.
- Second-order parabolic equations
- Sobolev spaces
- Vanishing mean oscillation
ASJC Scopus subject areas
- Applied Mathematics