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PreprintCC BY 4.0arXiv

Complex Dirichlet problem with unbounded boundary values

  • Huy Hoang Dao
  • Quang Dieu Nguyen
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Abstract

We study the Dirichlet problems with unbounded boundary data. Our main theorem proves interior continuity from a local biholomorphic deformation satisfying a one-sided compatibility condition near the infinite locus and barriers on the associated boundary cluster set. The deformed domains need not be nested, and the proof uses neither a Runge hypothesis nor a pseudoconvex ambient neighbourhood. We also prove nonmonotone Perron--Bremermann convergence outside an intrinsic neighbourhood pluripolar hull, a disk-fibre hull representation, stability under simultaneous nonmonotone variations of the domain and obstacle, and uniqueness in a fixed obstacle class.

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Cite

BibTeXRIS
BibTeX
@misc{dao2026complex,
  title = {{Complex Dirichlet problem with unbounded boundary values}},
  author = {Huy Hoang Dao and Quang Dieu Nguyen},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.00914},
  eprint = {2610.00914},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.00914},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Complex Dirichlet problem with unbounded boundary values
AU  - Huy Hoang Dao
AU  - Quang Dieu Nguyen
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.00914
UR  - https://arxiv.org/abs/2610.00914
AB  - We study the Dirichlet problems with unbounded boundary data. Our main theorem proves interior continuity from a local biholomorphic deformation satisfying a one-sided compatibility condition near the infinite locus and barriers on the associated boundary cluster set. The deformed domains need not be nested, and the proof uses neither a Runge hypothesis nor a pseudoconvex ambient neighbourhood. We also prove nonmonotone Perron--Bremermann convergence outside an intrinsic neighbourhood pluripolar hull, a disk-fibre hull representation, stability under simultaneous nonmonotone variations of the domain and obstacle, and uniqueness in a fixed obstacle class.
ER  -