Publikation: Sharp Trace and Korn Inequalities for Differential Operators
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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 Calderón-Zygmund theory, we prove that sharp trace estimates can be systematically reduced to full k-th order gradient estimates. Moreover, for 1 < p < ∞, where sharp trace estimates yield Korn-type inequalities on smooth domains, we show for the basically optimal class of John domains that Korn-type inequalities persist – even though the reduction to global Calderón-Zygmund estimates by extension operators might not be possible.
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DIENING, Lars, Franz GMEINEDER, 2024. Sharp Trace and Korn Inequalities for Differential Operators. In: Potential Analysis. Springer. ISSN 0926-2601. eISSN 1572-929X. Verfügbar unter: doi: 10.1007/s11118-024-10165-1BibTex
@article{Diening2024-10-02Sharp-71206, year={2024}, doi={10.1007/s11118-024-10165-1}, title={Sharp Trace and Korn Inequalities for Differential Operators}, issn={0926-2601}, journal={Potential Analysis}, author={Diening, Lars and Gmeineder, Franz} }
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