Abstract
We address three related problems in the theory of elasticity, formulated in the framework of double forms: the Saint-Venant compatibility condition, the existence and uniqueness of solutions for equations arising in incompatible elasticity, and the existence of stress potentials. The scope of this work is for manifolds with boundary of arbitrary dimension, having constant sectional curvature. The central analytical machinery is the regular ellipticity of a boundary-value problem for a bilaplacian operator, and its consequences, which were developed in [R. Kupferman and R. Leder, arXiv:2103.16823, 2021]. One of the novelties of this work is that stress potentials can be used in non-Euclidean geometries, and that the gauge freedom can be exploited to obtain a generalization for the biharmonic equation for the stress potential in dimensions greater than two.
| Original language | English |
|---|---|
| Pages (from-to) | 4625-4657 |
| Number of pages | 33 |
| Journal | SIAM Journal on Mathematical Analysis |
| Volume | 54 |
| Issue number | 4 |
| DOIs | |
| State | Published - 2022 |
Bibliographical note
Publisher Copyright:© 2022 Society for Industrial and Applied Mathematics.
Keywords
- Saint-Venant compatibility
- differential geometry
- double forms
- elasticity
- partial differential equations
- stress potentials