Published Paper

Inserted: 27 jan 2014
Last Updated: 13 may 2015

Journal: Ann. Mat. Pura Appl. (4)
Volume: 194
Number: 3
Pages: 645-671
Year: 2015
Doi: 10.1007/s10231-013-0392-0

Abstract:

In this paper, we establish the local Hölder continuity of the spatial gradient of the solution $u$ to the parabolic obstacle problem with superquadratic growth. More precisely, we prove that \[Du\in C^{0;\alpha,\frac{\alpha}{2}}_\text{loc}~~~\text{for some}~\alpha\in(0,1),\] provided the coefficients and the obstacle are regular enough.