Variational competition between the full Hessian and its determinant for convex functions
(2024) Nonlinear Analysis — Vol. 242, p. 113498 (2024)
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- Abstract
- We prove upper and lower bounds for a variational functional for convex functions satisfying certain boundary conditions on a sector of the unit ball in two dimensions. The functional contains two terms: The full Hessian and its determinant, where the former is treated as a small perturbation in the space L^2 and the latter as the leading-order term, in the negative Sobolev space W^{−2,2}. We point out how this setting is motivated by problems in nonlinear elasticity, and obtain a corollary for a variational problem based on the so-called Föppl-von-Kármán energy.
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Gladbach, P., & Olbermann, H. (2024). Variational competition between the full Hessian and its determinant for convex functions. Nonlinear Analysis, 242, 113498. https://hdl.handle.net/2078.5/236499 (Original work published 2024)