University of Pittsburgh

url: http://www.pitt.edu/~manfredi

**Abstract**: Consider the parabolic -Laplacian equation

We study the regularity of the

for all test functions . Here is the underlying domain in and is a bounded viscosity supersolution in . The first step of our proof is to establish the above inequality for the so-called infimal convolution . The function has the advantage of being differentiable with respect to all its variables , and , while the original is merely lower semicontinuous to begin with. The second step is to pass to the limit as . It is clear that but it is delicate to establish a sufficiently good convergence of the 's.

This is joint work with Peter Lindqvist at Trondheim (Norway).