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Higher order parabolic boundary Harnack inequality in C1 and Ck, α domains

The author has received funding from the European Research Council (ERC) under the Grant Agreement No 801867, and from the Swiss National Science Foundation project 200021_178795

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  • 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.

    Mathematics Subject Classification: Primary: 35K10; Secondary: 35R35.


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