Fourth Order Saint-Venant Inequalities: Maximizing Compliance and Mean Deflection Among Clamped Plates
Abstract We prove a fourth order analogue of the Saint-Venant inequality: the mean deflection of a clamped plate under uniform transverse load is maximal for the ball, among plates of prescribed volume in any dimension of space. The method works in the Euclidean space, the hyperbolic space, and the sphere. Similar results for clamped plates under small compression and for the compliance under non-uniform loads are proved to hold in two dimensional Euclidean space, with the higher dimensional and curved cases of those problems left open.
Authors
- Richard S. Laugesen (ORCID: https://orcid.org/0000-0003-1106-7203)
- Roméo Leylekian (ORCID: https://orcid.org/0000-0002-9277-0437)
- Dorin Bucur (ORCID: https://orcid.org/0000-0002-8331-8481)
- Mark S. Ashbaugh
Institutions
- Centre National de la Recherche Scientifique (FR)
- University of Lisbon (PT)
- University of Illinois Urbana-Champaign (US)
- Laboratoire d’Analyse et de Mathématiques Appliquées (FR)
- Université Savoie Mont Blanc (FR)
- University of Missouri (US)
Publication Details
- Journal
- Communications in Mathematical Physics
- Published
- 2025-09-01
- DOI
- https://doi.org/10.1007/s00220-025-05439-7
- Citations
- 1
- Primary Topic
- Contact Mechanics and Variational Inequalities
- Type
- article
- Field-Weighted Citation Impact
- 1.50
Funders
- National Science Foundation
- Simons Foundation
- Fundação para a Ciência e a Tecnologia
- Division of Mathematical Sciences