Regularity estimates for singular parabolic measure data problems with sharp growth

Abstract

We prove global gradient estimates for parabolic $p$-Laplace type equations with measure data, whose model is $$u_t-\text{div}\left(|Du{|}^{p-2}Du\right)=\mu \text{in}\Omega \times (0,T)\subset {\mathbb{R}}^n\times \mathbb{R},$$ where $\mu$ is a signed Radon measure with finite total mass. We consider the singular case $$\frac{2n}{n+1}<p\le 2-\frac{1}{n+1}$$ and give possibly minimal conditions on the nonlinearity and the boundary of $\Omega$, which guarantee the regularity results for such measure data problems.

30 pages

References in corpus (3)

• Renormalized solutions of nonlinear parabolic equations with general measure data
• Diffuse measures and nonlinear parabolic equations
• Gradient estimates for singular parabolic $p$-Laplace type equations with measure data

Cited by in corpus (1)

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