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BV-Regularity of the Boltzmann Equation in Non-Convex Domains

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Abstract

We consider the Boltzmann equation in a general non-convex domain with the diffuse boundary condition. We establish optimal BV estimates for such solutions. Our method consists of a new W 1,1-trace estimate for the diffuse boundary condition and a delicate construction of an \({\varepsilon}\)-tubular neighborhood of the singular set.

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References

  1. Cercignani C., Illner R., Pulvirenti M.: The Mathematical Theory of Dilute Gases. Applied Mathematical Sciences, vol. 106. Springer, New York (1994)

    Book  MATH  Google Scholar 

  2. Esposito R., Guo Y., Kim C., Marra R.: Non-Isothermal Boundary in the Boltzmann Theory and Fourier Law. Commun. Math. Phys. 323, 177–239 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. Evans L., Gariepy R.: Measure Theory and Fine Properties of Functions. CRC Press, Boca Raton (1991)

    MATH  Google Scholar 

  4. Guo Y.: Singular solutions of the Vlasov–Maxwell system on a half line. Arch. Ration. Mech. Anal. 131, 241–304 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  5. Guo Y.: Decay and continuity of Boltzmann equation in bounded domains. Arch. Ration. Mech. Anal. 197, 713–809 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  6. Guo, Y., Kim, C., Tonon, D., Trescases, A.: Regularity of the Boltzmann equation in convex domains. arXiv:1212.1694 (submitted)

  7. Kim C.: Formation and propagation of discontinuity for Boltzmann equation in non-convex domains. Commun. Math. Phys. 308, 641–701 (2011)

    Article  ADS  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Division of Applied Mathematics, Brown University, Providence, RI, 02812, USA

    Y. Guo

  2. Department of Mathematics, University of Wisconsin, Madison, WI, 53706, USA

    C. Kim

  3. CEREMADE, Université Paris Dauphine, Place du Maréchal De Lattre De Tassigny, 75775, Paris, France

    D. Tonon

  4. CMLA, ENS Cachan, 61, avenue du Président Wilson, 94235, Cachan, France

    A. Trescases

Authors
  1. Y. Guo
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  2. C. Kim
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  3. D. Tonon
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  4. A. Trescases
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Corresponding author

Correspondence to C. Kim.

Additional information

Communicated by L. Saint-Raymond

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Guo, Y., Kim, C., Tonon, D. et al. BV-Regularity of the Boltzmann Equation in Non-Convex Domains. Arch Rational Mech Anal 220, 1045–1093 (2016). https://doi.org/10.1007/s00205-015-0948-9

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  • DOI: https://doi.org/10.1007/s00205-015-0948-9

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