Higher order parabolic boundary Harnack inequality in C1 and Ck, α domains
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<p style='text-indent:20px;'>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 <i>C</i><sup>1</sup> and <i>C</i><sup><i>k</i>, <i>α</i></sup> domains, providing that the quotient of two solutions vanishing on the boundary of the domain is as smooth as the boundary.</p><p style='text-indent:20px;'>As a consequence of our result, we provide a new proof of higher order regularity of the free boundary in the parabolic obstacle problem.</p>
2020 ◽
Vol 26
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pp. 37
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2021 ◽
Vol 502
(3)
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pp. 3976-3992
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1994 ◽
Vol 36
(2)
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pp. 213-233
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2004 ◽
Vol 14
(08)
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pp. 2979-2990
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