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arXiv · 2306.01636

Generalized Monge-Amp\`ere functionals and related variational problems

Freid Tong·Shing-Tung Yau
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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.

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Freid Tong, Shing-Tung Yau. 2023-06-02. Generalized Monge-Amp\`ere functionals and related variational problems. https://arxiv.org/abs/2306.01636

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