𝐿^{∞}-regularity for a wide class of parabolic systems with general growth
Teresa Isernia · Proceedings of the American Mathematical Society · 2018
We prove the local boundedness of weak solutions for the following non-linear second order parabolic systems: u t − d i v ( φ ′ ( | D u | ) | D u | D u ) = 0 in Ω T := Ω × ( − T , 0 ) , \begin{equation*} u_{t} - \mathrm {div} \left ( \frac {\mathcal {\varphi }’(|Du|)}{|Du|}Du\right )=0 \mbox { in } \Omega _{T}:=\Omega \times (-T,0), \end{equation*} where Ω ⊂ R n \Omega \subset \mathbb {R}^{n} is a bounded domain and φ \mathcal {\varphi } is a given N N -function. The proof of this result is based on a Moser-type iteration argument.