Skip to content
DraconiticResearch
Search Sources API
203,203 studies31 sourcesUpdated 3 min ago
PreprintarXiv licencearXiv

A rigidity result for a global vectorial free boundary problem with a linear datum

  • Giovanni Siclari
  • Bozhidar Velichkov
Open at sourcePDFDOICite

Abstract

In this paper we completely classify the minimizers of a measure constraint global vectorial free boundary problem with a linear datum. More precisely, we show that there exists a unique minimizer whose coincidence set is an ellipsoid. We are motivated by the connection of the problem with the blow-ups of the vectorial Bernoulli free boundary problem and the obstacle problem.

Related

  1. Boundary Cases of the J-Equation: Divisorial Rigidity and a Global C0 Estimate
    Jixiang Fu, Ziyi Zhang
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv
  2. Global nonlinear stability of the plasma-vacuum free boundary problem for the 2D ideal incompressible MHD
    Yuan Cai
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  3. A Liouville type rigidity result for entire solutions of the k-Hessian equation
    Bin Wang
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  4. Boundary asymptotics for two-dimensional vectorial Allen-Cahn systems
    Zhiyuan Dai, Haotong Fu, Huaijie Wang +1
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsGeometry & topologyarXiv
  5. A rigidity result for the weighted p-Laplace equation in higher dimensions
    Ching-Lung Lin, Yi-Hsuan Lin
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@misc{siclari2026rigidity,
  title = {{A rigidity result for a global vectorial free boundary problem with a linear datum}},
  author = {Giovanni Siclari and Bozhidar Velichkov},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.34747},
  eprint = {2609.34747},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.34747},
}
RIS
TY  - UNPB
TI  - A rigidity result for a global vectorial free boundary problem with a linear datum
AU  - Giovanni Siclari
AU  - Bozhidar Velichkov
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.34747
UR  - https://arxiv.org/abs/2609.34747
AB  - In this paper we completely classify the minimizers of a measure constraint global vectorial free boundary problem with a linear datum. More precisely, we show that there exists a unique minimizer whose coincidence set is an ellipsoid. We are motivated by the connection of the problem with the blow-ups of the vectorial Bernoulli free boundary problem and the obstacle problem.
ER  -