Journal
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
Volume 42, Issue 6, Pages 2667-2698Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcds.2021207
Keywords
Parabolic equations; boundary Harnack; free boundary; boundary regularity; higher regularity
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Funding
- European Research Council (ERC) [801867]
- Swiss National Science Foundation [200021_178795]
- European Research Council (ERC) [801867] Funding Source: European Research Council (ERC)
- Swiss National Science Foundation (SNF) [200021_178795] Funding Source: Swiss National Science Foundation (SNF)
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We study the boundary behavior of solutions to second order parabolic linear equations in moving domains. Our main result is a higher order boundary Harnack inequality in C-1 and C-k,C-alpha domains, showing that the quotient of two solutions vanishing on the boundary of the domain is as smooth as the boundary. As a consequence, we provide a new proof of higher order regularity of the free boundary in the parabolic obstacle problem.
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 C-1 and C-k,C-alpha 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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