### Sharp trace and Korn inequalities for differential operators

Diening L, Gmeineder F (2021)
arXiv:2105.09570.

Preprint | Englisch

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Autor*in
Diening, LarsUniBi ; Gmeineder, Franz
Einrichtung
Abstract / Bemerkung
We establish sharp trace- and Korn-type inequalities that involve vectorial differential operators, the focus being on situations where global singular integral estimates are not available. Starting from a novel approach to sharp Besov boundary traces by Riesz potentials and oscillations that equally applies to $p=1$, a case difficult to be handled by harmonic analysis techniques, we then classify boundary trace- and Korn-type inequalities. For $p=1$ and so despite the failure of the Calder\'{o}n-Zygmund theory, we prove that sharp trace estimates can be systematically reduced to full $k$-th order gradient estimates. Moreover, for \$1
Erscheinungsjahr
2021
Zeitschriftentitel
arXiv:2105.09570
Page URI
https://pub.uni-bielefeld.de/record/2955042

### Zitieren

Diening L, Gmeineder F. Sharp trace and Korn inequalities for differential operators. arXiv:2105.09570. 2021.
Diening, L., & Gmeineder, F. (2021). Sharp trace and Korn inequalities for differential operators. arXiv:2105.09570
Diening, L., and Gmeineder, F. (2021). Sharp trace and Korn inequalities for differential operators. arXiv:2105.09570.
Diening, L., & Gmeineder, F., 2021. Sharp trace and Korn inequalities for differential operators. arXiv:2105.09570.
L. Diening and F. Gmeineder, “Sharp trace and Korn inequalities for differential operators”, arXiv:2105.09570, 2021.
Diening, L., Gmeineder, F.: Sharp trace and Korn inequalities for differential operators. arXiv:2105.09570. (2021).
Diening, Lars, and Gmeineder, Franz. “Sharp trace and Korn inequalities for differential operators”. arXiv:2105.09570 (2021).

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### Quellen

arXiv: 2105.09570