Optimal function spaces for continuity of the Hessian determinant as a distribution
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1411.5303.pdf
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Author(s)
Baer, Eric
Jerison, David S
Date Issued
September 2015
Journal
Journal of Functional Analysis
Publisher
Elsevier BV
Citation
Baer, Eric, and David Jerison. “Optimal Function Spaces for Continuity of the Hessian Determinant as a Distribution.” Journal of Functional Analysis, vol. 269, no. 5, Sept. 2015, pp. 1482–514.
Version
Original manuscript
Abstract
We establish optimal continuity results for the action of the Hessian determinant on spaces of Besov type into the space of distributions on R[superscript 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(2-2/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(2-2/N,N) as the space of traces of functions in the Sobolev space W[superscript 2,N](R[superscript N+2]) on the subspace R[superscript N] of codimension 2. The most delicate and elaborate part of the analysis is the construction of a counterexample to continuity in B(2-2/N,p) with p > N.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-NonCommercial-NoDerivs License
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DOI of Published Version
https://doi.org/10.1016/J.JFA.2015.05.001
