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On Besov Regularity of Temperatures

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Abstract

We prove space-time parabolic Besov regularity in terms of integrability of Besov norms in the space variable for solutions of the heat equation on cylindrical regions based on Lipschitz domains.

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References

  1. Aimar, H., Gómez, I., Iaffei, B.: Parabolic mean values and maximal estimates for gradients of temperatures. J. Funct. Anal. 255(8), 1939–1956 (2008)

    MATH  MathSciNet  Google Scholar 

  2. Bennett, C., Sharpley, R.: Interpolation of Operators. Pure and Applied Mathematics, vol. 129. Academic Press, San Diego (1988)

    MATH  Google Scholar 

  3. Bergh, J., Löfström, J.: Interpolation Spaces. An Introduction. Grundlehren der Mathematischen Wissenschaften, vol. 223. Springer, Berlin (1976)

    MATH  Google Scholar 

  4. Besov, O.V., Il’in, V.P., Nikol’skiĭ, S.M.: Integral Representations of Functions and Imbedding Theorems. Scripta Series in Mathematics, vols. I, II. V.H. Winston & Sons, Washington (1978). Edited by Mitchell H. Taibleson

    MATH  Google Scholar 

  5. Dahlke, S., DeVore, R.A.: Besov regularity for elliptic boundary value problems. Commun. Partial Differ. Equ. 22(1–2), 1–16 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  6. Han, Y.S., Sawyer, E.T.: Littlewood-Paley theory on spaces of homogeneous type and the classical function spaces. Mem. Am. Math. Soc. 110(53), vi–126 (1994)

    MathSciNet  Google Scholar 

  7. Jakab, T., Mitrea, M.: Parabolic initial boundary value problems in nonsmooth cylinders with data in anisotropic Besov spaces. Math. Res. Lett. 13(5–6), 825–831 (2006)

    MATH  MathSciNet  Google Scholar 

  8. Jerison, D., Kenig, C.E.: The inhomogeneous Dirichlet problem in Lipschitz domains. J. Funct. Anal. 130(1), 161–219 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  9. Peetre, J.: New Thoughts on Besov Spaces. Duke University Mathematics Series, vol. 1. Mathematics Department, Duke University, Durham (1976)

    MATH  Google Scholar 

  10. Schmeisser, H.-J.: Anisotropic spaces. II. Equivalent norms for abstract spaces, function spaces with weights of Sobolev-Besov type. Math. Nachr. 79, 55–73 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  11. Schmeisser, H.-J., Triebel, H.: Anisotropic spaces. I. Interpolation of abstract spaces and function spaces. Math. Nachr. 73, 107–123 (1976)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. IMAL–FIQ (CONICET-UNL), Güemes, 3450–S3000GLN, Argentina

    Hugo Aimar & Ivana Gómez

  2. IMAL–FHUC (CONICET-UNL), Güemes, 3450–S3000GLN, Argentina

    Bibiana Iaffei

Authors
  1. Hugo Aimar
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  2. Ivana Gómez
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  3. Bibiana Iaffei
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Corresponding author

Correspondence to Ivana Gómez.

Additional information

Communicated by Stephan Dahlke.

The research was supported by CONICET, UNL and ANPCyT, Argentina.

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Aimar, H., Gómez, I. & Iaffei, B. On Besov Regularity of Temperatures. J Fourier Anal Appl 16, 1007–1020 (2010). https://doi.org/10.1007/s00041-010-9134-5

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  • DOI: https://doi.org/10.1007/s00041-010-9134-5

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