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Korn and Poincaré-Korn inequalities for thin domains in GSBDp

  • Davit Harutyunyan
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Abstract

We prove Korn's first inequalities with and without boundary conditions in GSBDp (1<p<∞) in C1,1-regular thin domains with Lipschitz thickness boundaries with a constant C h−p, that is optimal if the domain mid-surface contains a flat region, e.g., if the domain contains a piece of plate. For the one with boundary condition, we impose zero Dirichlet boundary conditions on the thin lateral faces of the shell, where we prove that the same estimate holds with no subtracted rigid motion like in the classical case for Sobolev vector fields.

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Cite

BibTeXRIS
BibTeX
@misc{harutyunyan2026korn,
  title = {{Korn and Poincaré-Korn inequalities for thin domains in $GSBD^p$}},
  author = {Davit Harutyunyan},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.21261},
  eprint = {2609.21261},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.21261},
}
RIS
TY  - UNPB
TI  - Korn and Poincaré-Korn inequalities for thin domains in GSBD^p
AU  - Davit Harutyunyan
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2609.21261
UR  - https://arxiv.org/abs/2609.21261
AB  - We prove Korn's first inequalities with and without boundary conditions in GSBD^p (1<p<∞) in C^1,1-regular thin domains with Lipschitz thickness boundaries with a constant C h^−p, that is optimal if the domain mid-surface contains a flat region, e.g., if the domain contains a piece of plate. For the one with boundary condition, we impose zero Dirichlet boundary conditions on the thin lateral faces of the shell, where we prove that the same estimate holds with no subtracted rigid motion like in the classical case for Sobolev vector fields.
ER  -