Elliptic problems with rough boundary data in generalized Sobolev spaces

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2021
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Murach, Aleksandr
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Communications on Pure & Applied Analysis. American Institute of Mathematical Sciences (AIMS). 2021, 20(2), pp. 697-735. ISSN 1534-0392. eISSN 1553-5258. Available under: doi: 10.3934/cpaa.2020286
Zusammenfassung

We investigate regular elliptic boundary-value problems in boun-ded domains and show the Fredholm property for the related operators in an extended scale formed by inner product Sobolev spaces (of arbitrary real orders) and corresponding interpolation Hilbert spaces. In particular, we can deal with boundary data with arbitrary low regularity. In addition, we show interpolation properties for the extended scale, embedding results, and global and local a priori estimates for solutions to the problems under investigation. The results are applied to elliptic problems with homogeneous right-hand side and to elliptic problems with rough boundary data in Nikolskii spaces, which allows us to treat some cases of white noise on the boundary.

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510 Mathematik
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ISO 690ANOP, Anna, Robert DENK, Aleksandr MURACH, 2021. Elliptic problems with rough boundary data in generalized Sobolev spaces. In: Communications on Pure & Applied Analysis. American Institute of Mathematical Sciences (AIMS). 2021, 20(2), pp. 697-735. ISSN 1534-0392. eISSN 1553-5258. Available under: doi: 10.3934/cpaa.2020286
BibTex
@article{Anop2021Ellip-53404,
  year={2021},
  doi={10.3934/cpaa.2020286},
  title={Elliptic problems with rough boundary data in generalized Sobolev spaces},
  number={2},
  volume={20},
  issn={1534-0392},
  journal={Communications on Pure & Applied Analysis},
  pages={697--735},
  author={Anop, Anna and Denk, Robert and Murach, Aleksandr}
}
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