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• W1565014698 abstract "We establish optimal continuity results for the action of the Hessian determinant on spaces of Besov type into the space of distributions on $mathbb{R}^N$. In particular, inspired by recent work of Brezis and Nguyen on the distributional Jacobian determinant, we show that the action is continuous on the Besov space of fractional order $B(2-frac{2}{N},N)$, and that all continuity results in this scale of Besov spaces are consequences of this result. A key ingredient in the argument is the characterization of $B(2-frac{2}{N},N)$ as the space of traces of functions in the Sobolev space $W^{2,N}(mathbb{R}^{N+2})$ on the subspace $mathbb{R}^N$ of codimension $2$. The most delicate and elaborate part of the analysis is the construction of a counterexample to continuity in $B(2-frac{2}{N},p)$ with $p>N$." @default.
• W1565014698 created "2016-06-24" @default.
• W1565014698 creator A5033260292 @default.
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• W1565014698 date "2014-11-19" @default.
• W1565014698 modified "2023-09-27" @default.
• W1565014698 title "Optimal function spaces for continuity of the Hessian determinant as a distribution" @default.
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• W1565014698 hasPublicationYear "2014" @default.
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