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Regularity in Besov spaces of parabolic PDEs

By Cornelia Schneider

Appears in collection : Geometry and analysis on non-compact manifolds / Géométrie et analyse sur les variétés non compactes

This talk is concerned with the regularity of solutions to parabolic evolution equations. Special attention is paid to the smoothness in the specific scales $\ B^{r}_{\tau,\tau}, \ \frac{1}{\tau}=\frac{r}{d}+\frac{1}{p}\ $ of Besov spaces. The regularity in these spaces determines the approximation order that can be achieved by fully space-time adaptive approximation schemes.

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Citation data

  • DOI 10.24350/CIRM.V.19902603
  • Cite this video Schneider Cornelia (3/28/22). Regularity in Besov spaces of parabolic PDEs. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19902603
  • URL https://dx.doi.org/10.24350/CIRM.V.19902603

Bibliography

  • DAHLKE, Stephan et SCHNEIDER, Cornelia. Besov regularity of parabolic and hyperbolic PDEs. Analysis and Applications, 2019, vol. 17, no 02, p. 235-291. - https://arxiv.org/abs/1811.09428
  • DAHLKE, Stephan et SCHNEIDER, Cornelia. Regularity in Sobolev and Besov spaces for parabolic problems on domains of polyhedral type. The Journal of Geometric Analysis, 2021, vol. 31, no 12, p. 11741-11779. - https://arxiv.org/abs/2105.12796
  • DAHLKE, Stephan et SCHNEIDER, Cornelia. Anisotropic Besov regularity of parabolic PDEs. arXiv preprint arXiv:2112.09485, 2021. - https://arxiv.org/abs/2112.09485

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