Boundary behavior of solutions to the parabolic p-Laplace equation

摘要

We establish boundary estimates for non-negative solutions to the p-parabolicequation in the degenerate range $p>2$. Our main results include new parabolicintrinsic Harnack chains in cylindrical NTA-domains together with sharpboundary decay estimates. If the underlying domain is $C^{1,1}$-regular, weestablish a relatively complete theory of the boundary behavior, includingboundary Harnack principles and H\"older continuity of the ratios of twosolutions, as well as fine properties of associated boundary measures. There isan intrinsic waiting time phenomena present which plays a fundamental rolethroughout the paper. In particular, conditions on these waiting times rule outwell-known examples of explicit solutions violating the boundary Harnackprinciple.