The analysis of some three-dimensional optimal design problems leads us to study variational principles under curl-free and divergence-free constraints simultaneously. We explicitly exploit the relationship between curl-free and div-free restrictions in order to take advantage of the accumulated experience in the classical curl case by the introduction of potentials. Our discussion takes place in the three-dimensional situation. This is a first contribution in the sense that we only deal with the most basic issues. © 2003 Elsevier Inc. All rights reserved.
Bellido, J. C., & Pedregal, P. (2003). Optimal design via variational principles: The three-dimensional case. Journal of Mathematical Analysis and Applications, 287(1), 157–176. https://doi.org/10.1016/S0022-247X(03)00540-7