Boundary ellipticity and limiting L1-estimates on halfspaces
(2024) Advances in mathematics — Vol. 439, p. 109490 (2024)
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- We identify necessary and sufficient conditions on kth order differential operators A in terms of a fixed halfspace H+⊂Rn such that the Gagliardo–Nirenberg–Sobolev inequality ∥D^{k−1}u∥L^{n/(n−1)}(H+)≤c∥Au∥L¹(H+)for u∈C^∞_c(R^n,V) holds. This comes as a consequence of sharp trace theorems on H=∂H+.
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Gmeineder, F., Raiţă, B., & Van Schaftingen, J. (2024). Boundary ellipticity and limiting L1-estimates on halfspaces. Advances in mathematics, 439, 109490. https://doi.org/10.1016/j.aim.2024.109490 (Original work published 2024)