Global Hölder solvability for parabolic equations with interior Morrey data

Abstract

We prove global Hölder solvability for uniformly parabolic divergence-form equations with locally finite measure data under an interior Morrey growth condition and a capacity density condition on the spatial domain. The parabolic distance to the initial and lateral boundary is assumed bounded on the source support. For nonnegative data, we establish necessity results that demonstrate the sharpness of the growth and domain assumptions. We also derive estimates for divergence forcing, prove solvability for equations with lower-order terms, and obtain convergence rates in periodic homogenization.