Linear Parabolic Equations with a Singular Lower Order Coefficient.

摘要

This report was motivated by the study of free boundary value problems related to the Stefan problem. The precise description of the smoothness of the free boundary requires sharp regularity results for linear parabolic equations with singular coefficients. These results are of independent interest. They can be applied to parabolic equations on domains with curved boundaries that tough the x-axis. As a particular example consider the heat equation; this example arises in the convexity of the nonlinear parabolic problem.