Time derivative estimates for normalized parabolic $p$-Laplace equations

Abstract

We establish the local boundedness of time derivatives of bounded viscosity solutions to the normalized parabolic $p$-Laplace equation for every $p\in (1,\infty )$. The proof combines a logarithmic Bernstein argument with quantitative stability to derive a recursive estimate between different regularizations. For $p=1$ and $n\ge 2$, we construct a bounded viscosity solution which is not Hölder continuous in time with any positive exponent.

17 pages