Higher order parabolic boundary Harnack inequality in C1 and Ck,α domains
Abstract
We study the boundary behaviour of solutions to second order parabolic linear equations in moving domains. Our main result is a higher order boundary Harnack inequality in C1 and Ck,α domains, providing that the quotient of two solutions vanishing on the boundary of the domain is as smooth as the boundary. As a consequence of our result, we provide a new proof of higher order regularity of the free boundary in the parabolic obstacle problem.
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