Regularity results for nonlinear parabolic obstacle problems with subquadratic growth

In [26] it was shown that the spatial gradient of the solution u to the parabolic obstacle problem with superquadratic growth is local Hölder continuous provided the obstacle is regular enough. In this paper, we extend this regularity result to the subquadratic case. This means we establish the local Hölder continuity of the spatial gradient of the solution u to the parabolic obstacle problem with subquadratic growth. More precisely, we prove thatDu∈Cloc0;α,α2   for some α∈(0,1), provided the coefficients and the obstacle are regular enough. Moreover, we use the local Hölder continuity to prove the local Lipschitz continuity of the solution u, i.e.u∈Cloc0;1,12.