Marcinkiewicz regularity for singular parabolic $p$-Laplace type equations with measure data

Jung-Tae Park

doi:10.1016/j.na.2022.113073

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arXiv · 2107.09322

Marcinkiewicz regularity for singular parabolic $p$-Laplace type equations with measure data

Jung-Tae Park

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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: $$u_t - \textrm{div} \, \mathbf{a}(Du,x,t) = μ\quad \textrm{in} \ Ω\times (0,T) \subset \mathbb{R}^n \times \mathbb{R}.$$ In the singular range $\frac{2n}{n+1} <p \le 2-\frac{1}{n+1}$, 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.

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BibTeX RIS

Jung-Tae Park. 2022-07-20. Marcinkiewicz regularity for singular parabolic $p$-Laplace type equations with measure data. https://doi.org/10.1016/j.na.2022.113073

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