A Counterexample to C^2,1 Regularity for Parabolic Fully Nonlinear Equations

Abstract

We address the self-similar solvability of a singular parabolic problem and show that solutions to parabolic fully nonlinear equations are not expected to be C ^2,1.

Keywords:

• Fully nonlinear parabolic equation
• Regularity
• Self-similar solutions

Mathematics Subject Classification:

• 35K55

Acknowledgments

Ulisse Stefanelli gratefully acknowledges the hospitality of the Department of Mathematics and the Institute for Computational Engineering and Sciences of the University of Texas at Austin, where most of this research was performed.