A necessary and sufficient condition for H\"{o}lder-class solutions to the complex Monge--Amp\`{e}re equation

Annapurna Banik

A necessary and sufficient condition for H\"{o}lder-class solutions to the complex Monge--Amp\`{e}re equation

Complex Variables 2025-11-25 v1 Analysis of PDEs

Authors: Annapurna Banik

Abstract

We provide a necessary and sufficient condition for the existence of H\"{o}lder continuous solutions to the complex Monge--Amp\`{e}re equation on bounded domains in $\mathbb{C}^n$ . This condition is motivated by a paper by S.-Y. Li. We also prove a result on the regularity of solutions to the complex Monge--Amp\`{e}re equation on general $B$ -regular domains in $\mathbb{C}^n$ .

Keywords

latent safety filter Hamilton-Jacobi reachability control barrier function smooth safety filtering hard-to-model constraints

Cite

@article{arxiv.2511.18605,
  title  = {A necessary and sufficient condition for H\"{o}lder-class solutions to the complex Monge--Amp\`{e}re equation},
  author = {Annapurna Banik},
  journal= {arXiv preprint arXiv:2511.18605},
  year   = {2025}
}

Comments

9 pages; Comments welcome!

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