PreprintCC BY 4.0arXiv
Generic variational principles for supinf problems with constraints
Abstract
We study supinf problems for perturbations of a given function of two variables by continuous bounded functions in the underlying spaces and the properties of the associated solution mapping. We provide conditions on the initial data such that most (in the Baire category sense) of the functions from the perturbation space secure existence and uniqueness of the solution of the supinf problem for the corresponding perturbed functions. In this way we obtain generic variational principles for such problems.
Related
- First-order Methods for Variational Inequality Problems with Semi-Infinite Constraints
- Metric gradient flows and variational principles
- A new perspective in linear Cauchy Elasticity: variational minimum principles for statics, dynamics, and heterogeneous materials
- Rough variational principles and applications to adjoint systems
- A priori bounds for geodesic diameter. Part III. A Sobolev–Poincaré inequality and applications to a variety of geometric variational problems
BibTeX
@misc{gaumont2026generic,
title = {{Generic variational principles for supinf problems with constraints}},
author = {D. Gaumont and D. Kamburova and J. P. Revalski},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28289},
eprint = {2609.28289},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28289},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Generic variational principles for supinf problems with constraints
AU - D. Gaumont
AU - D. Kamburova
AU - J. P. Revalski
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28289
UR - https://arxiv.org/abs/2609.28289
AB - We study supinf problems for perturbations of a given function of two variables by continuous bounded functions in the underlying spaces and the properties of the associated solution mapping. We provide conditions on the initial data such that most (in the Baire category sense) of the functions from the perturbation space secure existence and uniqueness of the solution of the supinf problem for the corresponding perturbed functions. In this way we obtain generic variational principles for such problems.
ER -