Towards an L1-theory for vector-valued elliptic boundary value problems

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2003
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Hieber, Matthias
Prüss, Jan
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IANNELLI, Mimmo, ed. and others. Evolution Equations : Applications to Physics, Industry, Life Sciences and Economics. Basel: Birkhäuser, 2003, pp. 141-147. Available under: doi: 10.1007/978-3-0348-8085-5_10
Zusammenfassung

In this note, we consider vector-valued boundary value problems with constant coefficients in the L1-setting for a half space. We assume the Lopatinskii-Shapiro condition to be true and obtain a representation of the solution u of the elliptic problem by integral operators which allows to deduce a-priori estimates for u in the L1-norm. These estimates imply in particular that the L1-realization of an elliptic boundary value problem with constant coefficients in the half space generates an analytic C0-semigroup.

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510 Mathematik
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ISO 690DENK, Robert, Matthias HIEBER, Jan PRÜSS, 2003. Towards an L1-theory for vector-valued elliptic boundary value problems. In: IANNELLI, Mimmo, ed. and others. Evolution Equations : Applications to Physics, Industry, Life Sciences and Economics. Basel: Birkhäuser, 2003, pp. 141-147. Available under: doi: 10.1007/978-3-0348-8085-5_10
BibTex
@incollection{Denk2003Towar-575,
  year={2003},
  doi={10.1007/978-3-0348-8085-5_10},
  title={Towards an L1-theory for vector-valued elliptic boundary value problems},
  publisher={Birkhäuser},
  address={Basel},
  booktitle={Evolution Equations : Applications to Physics, Industry, Life Sciences and Economics},
  pages={141--147},
  editor={Iannelli, Mimmo},
  author={Denk, Robert and Hieber, Matthias and Prüss, Jan}
}
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