Global higher integrability for non-quadratic parabolic quasi-minimizers on metric measure spaces.

We prove up-to-the-boundary higher integrability estimates for parabolic quasi-minimizers on a domain ΩT = × (0, T), where Ω denotes an open domain in a doubling metric measure space which supports a Poincaré inequality. The higher integrability for upper gradients is shown globally and under optimal conditions on the boundary ∂Ω of the domain as well as on the boundary data itself. This is a starting point for a further discussion on parabolic quasi-minima on metric measure spaces, such as for example regularity or stability issues. [ABSTRACT FROM AUTHOR]