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On Linear Elliptic and Parabolic Problems in Nikol’skij Spaces

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Parabolic Problems

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 80))

Abstract

We consider estimates depending on a parameter for general linear elliptic boundary value problems, with nonhomogeneous boundary conditions, in Nikol’skij spaces. These estimates are then employed to study general linear nonautonomous parabolic systems, again with nonhomogeneous boundary conditions. Maximal regularity results are proved.

Mathematics Subject Classification (2000). 35K30; 35J40; 46B70.

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Author information

Authors and Affiliations

  1. Dipartimento di matematica, Piazza di Porta S. Donato 5, I-40126, Bologna, Italy

    Davide Guidetti

Authors
  1. Davide Guidetti
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Corresponding author

Correspondence to Davide Guidetti .

Editor information

Editors and Affiliations

  1. Inst. Angewandte Mathematik, Leibniz Universität Hannover, Welfengarten 1, Hannover, 30167, Germany

    Joachim Escher

  2. School of Physical Sciences, Dept. Mathematics, University of California, Irvine, Irvine, 92697-3875, California, USA

    Patrick Guidotti

  3. , Fachbereich Mathematik, TU Darmstadt, Schlossgartenstr 7, Darmstadt, 64289, Germany

    Matthias Hieber

  4. Inst. Applied Mathematics & Mechanics, Warsaw University, ul. Banacha 2, Warszawa, 02-097, Poland

    Piotr Mucha

  5. , FB Mathematik und Informatik, Universität Halle-Wittenberg, Theodor-Lieser-Strasse 5, Halle, 06099, Germany

    Jan W. Prüss

  6. 3-4-1, Ohkubo Shinjuku-ku, Tokyo, 169-8555, Japan

    Yoshihiro Shibata

  7. , Deparment of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, TN 37240, USA

    Gieri Simonett

  8. Inst. Angewandte Mathematik, Leibniz Universität Hannover, Welfengarten 1, Hannover, 30167, Germany

    Christoph Walker

  9. Fac. Mathematics & Information Sciences, Warsaw University of Technology, pl. Politechniki 1, Warszawa, 00-661, Poland

    Wojciech Zajaczkowski

Additional information

Dedicated to professor Herbert Amann, in occasion of his seventieth birthday

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Guidetti, D. (2011). On Linear Elliptic and Parabolic Problems in Nikol’skij Spaces. In: Escher, J., et al. Parabolic Problems. Progress in Nonlinear Differential Equations and Their Applications, vol 80. Springer, Basel. https://doi.org/10.1007/978-3-0348-0075-4_15

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