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Higher order interp...
Abstract
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- We prove new optimal C1,α regularity results for obstacle problems involving evolutionary p-Laplace type operators in the degenerate regime p > 2. Our main results include the optimal regularity improvement at free boundary points in intrinsic backward p-paraboloids, up to the critical exponent, α ≤ 2/(p − 2), and the optimal regularity across the free boundaries in the full cylinders up to a universal threshold. Moreover, we provide an intrinsic criterion by which the optimal regularity improvement at free boundaries can be extended to the entire cylinders. An important feature of our analysis is that we do not impose any assumption on the time derivative of the obstacle. Our results are formulated in function spaces associated to what we refer to as higher order or C1,α intrinsic interpolative geometries.
Ämnesord
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
Nyckelord
- p-parabolic equation
- obstacle problem
- regularity
- intrinsic geometry
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- ref (ämneskategori)
- art (ämneskategori)
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