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PreprintCC BY 4.0arXiv

Global solutions to the fully nonlinear obstacle problem

  • Yi Cao
  • Dongsheng Li
Open at sourcePDFDOICite

Abstract

In this paper, we investigate global solutions to the fully nonlinear obstacle problem. We prove that, after factoring out invariant directions, the coincidence set of any global solution belongs to one of the following four types: a single point, a compact convex set with nonempty interior, a ray for n=1, or a slender body for n≥ 2, where n denotes the spatial dimension. Furthermore, we establish a bijection between the collection of all global solutions with compact coincidence sets and a family of functions describing the asymptotic behavior of such solutions at infinity.

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Cite

BibTeXRIS
BibTeX
@misc{cao2026global,
  title = {{Global solutions to the fully nonlinear obstacle problem}},
  author = {Yi Cao and Dongsheng Li},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.15313},
  eprint = {2610.15313},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.15313},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Global solutions to the fully nonlinear obstacle problem
AU  - Yi Cao
AU  - Dongsheng Li
PY  - 2026
DA  - 2026/10/11
PB  - arXiv
DO  - 10.48550/arxiv.2610.15313
UR  - https://arxiv.org/abs/2610.15313
AB  - In this paper, we investigate global solutions to the fully nonlinear obstacle problem. We prove that, after factoring out invariant directions, the coincidence set of any global solution belongs to one of the following four types: a single point, a compact convex set with nonempty interior, a ray for n=1, or a slender body for n≥ 2, where n denotes the spatial dimension. Furthermore, we establish a bijection between the collection of all global solutions with compact coincidence sets and a family of functions describing the asymptotic behavior of such solutions at infinity.
ER  -