| Abstract: |
| In this talk, we consider a parabolic $p$-Laplace type equation when the right-hand side is a signed Radon measure with finite total mass, whose model is
$$u_t - \textrm{div} \left(|Du|^{p-2} Du\right) = \mu \quad \textrm{in} \ \Omega \times (0,T) \subset \mathbb{R}^n \times \mathbb{R}.$$
In the singular range $\frac{2n}{n+1} < p \leq 2-\frac{1}{n+1}$, we discuss integrability results for the spatial gradient of a solution in the Marcinkiewicz space, under a suitable density condition of the right-hand side measure $\mu$. |
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