{
  "abstract": "Let Ω ⋐ C n be a bounded hyperconvex domain and ϕ : Ω → R a maximal plurisubharmonic function in Ω (possibly unbounded). We introduce a new class E 1 ϕ (Ω) of plurisubharmonic functions with boundary values equal to ϕ in the sense of Cegrell and finite ϕ-energy on Ω. Then given a Borel measure µ on Ω, we apply a variational approach to prove that µ is the Monge-Ampère measure of a function u ∈ E 1 ϕ (Ω) if and only if it satisfies the integrability condition\n\nWe also establish a quantitative version of this condition extending previous results of Cegrell and others. Using a logarithmic transformation, we obtain analogous results for the real Monge-Ampère equations with (unbounded) boundary data.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13478",
  "author_total": 4,
  "authors": [
    {
      "name": "Papa Badiane"
    },
    {
      "name": "Chinh H. Lu"
    },
    {
      "name": "Souhaibou Sambou"
    },
    {
      "name": "Ahmed Zeriahi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/etvsbs49hhksj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13478",
  "fulltext_url": null,
  "id": "etvsbs49hhksj",
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  "landing_url": "https://hal.science/hal-05787570v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "metadata_licence": "CC0-1.0",
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      "math.AP"
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  "openalex": "W7221488868",
  "pdf_url": "https://hal.science/hal-05787570/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/etvsbs49hhksj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:51Z",
      "native_id": "hal-05787570",
      "source": "hal",
      "url": "https://hal.science/hal-05787570v1"
    },
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.13478",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13478"
    }
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Complex Monge-Ampère equations with boundary values: a variational approach",
  "title_text": "Complex Monge-Ampère equations with boundary values: a variational approach",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/etvsbs49hhksj",
  "venue": "HAL",
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}