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arXiv · 1907.06109

Variational competition between full Hessian and its determinant for convex functions

Peter Gladbach·Heiner Olbermann
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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 F\"oppl-von-K\'arm\'an energy.

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Peter Gladbach, Heiner Olbermann. 2019-07-13. Variational competition between full Hessian and its determinant for convex functions. https://arxiv.org/abs/1907.06109

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