-
C1,α regularity of solutions to parabolic Monge-Ampére equations
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 134, Number 4, August 2012
- pp. 1051-1087
- 10.1353/ajm.2012.0030
- Article
- Additional Information
- Purchase/rental options available:
We study interior $C^{1, \alpha}$ regularity of viscosity solutions of the parabolic Monge-Amp\'ere equation
$$
u_t = b(x,t)\,\big(\!\det D^2 u\big)^p,
$$
with exponent $p >0$ and with coefficients $b$ which are bounded and measurable. We show that
when $p$ is less than the critical power $1\over{n-2}$ then solutions become instantly $C^{1,\alpha}$
in the interior. Also, we prove the same result for any power $p>0$ at those points where either the
solution separates from the initial data, or where the initial data is $C^{1,\beta}$.