Marcinkiewicz regularity for singular parabolic p-Laplace type equations with measure data. (October 2022) - Park, Jung-Tae
Abstract: We consider quasilinear parabolic equations with measurable coefficients when the right-hand side is a signed Radon measure with finite total mass, having p -Laplace type: u t − div a ( D u, x, t ) = μ in Ω × ( 0, T ) ⊂ R n × R . In the singular range 2 n n + 1 < p ≤ 2 − 1 n + 1, we establish regularity estimates for the spatial gradient of solutions in the Marcinkiewicz spaces, under a suitable density condition of the right-hand side measure.