Introduction to Regularity Theory for Degenerate Parabolic Equations in Divergence Form

Emmanuele DiBenedetto (Vanderbilt University, Nashville, USA)

Some recent techniques are introduced to investigate the local and global behavior of solutions of degenerate parabolic equations when their principal part fails to be coercive. The equations have to be regarded in their own intrinsic geometry, and the solutions have a limited degree of regularity. Identifying regularity classes as functions of the degenerate and/or singular structure of the PDE is part of an emerging theory which promises to yield an understanding of degeneracy and/or singularity in PDE's.