Generalized Monge-Amp\`ere functionals and related variational problems
Analysis of PDEs
2023-06-05 v1 Differential Geometry
Abstract
In this paper, we introduce a family of real Monge-Amp\`ere functionals and study their variational properties. We prove a Sobolev type inequality for these functionals and use this to study the existence and uniqueness of some associated Dirichlet problems. In particular, we prove the existence of solutions for a nonlinear eigenvalue problem associated to this family of functionals.
Cite
@article{arxiv.2306.01636,
title = {Generalized Monge-Amp\`ere functionals and related variational problems},
author = {Freid Tong and Shing-Tung Yau},
journal= {arXiv preprint arXiv:2306.01636},
year = {2023}
}
Comments
24 pages, comments welcome