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Parabolic Equations in Anisotropic Orlicz Spaces with General N-functions

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Parabolic Problems

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

Abstract

In the present paper we study the existence of weak solutions to an abstract parabolic initial-boundary value problem. On the operator appearing in the equation we assume the coercivity conditions given by an N-function (i.e., convex function satisfying conditions specified in the paper). The main novelty of the paper consists in the lack of any growth restrictions on the N-function combined with an anisotropic character of the N-function, namely we allow the dependence on all the directions of the gradient, not only on its absolute value.

Mathematics Subject Classification (2000). Primary 35K55; Secondary 35K20.

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Author information

Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics, University of Warsaw, Banacha 2, 02-097, Warsaw, Poland

    Piotr Gwiazda & Agnieszka Świerczewska Gwiazda

Authors
  1. Piotr Gwiazda
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  2. Agnieszka Świerczewska Gwiazda
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Corresponding author

Correspondence to Piotr Gwiazda .

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

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Gwiazda, P., Gwiazda, A.Ś. (2011). Parabolic Equations in Anisotropic Orlicz Spaces with General N-functions. 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_16

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