A gradient estimate for solutions to parabolic equations with discontinuous coefficients

Article, Preprint English OPEN
Jishan Fan; Kyoungsun Kim; Sei Nagayasu; Gen Nakamura;
  • Publisher: Texas State University
  • Journal: Electronic Journal of Differential Equations (issn: 1072-6691)
  • Publisher copyright policies & self-archiving
  • Subject: discontinuous coefficients | Mathematics | gradient estimate | Mathematics - Analysis of PDEs | QA1-939 | Parabolic equations

Li-Vogelius and Li-Nirenberg gave a gradient estimate for solutions of strongly elliptic equations and systems of divergence forms with piecewise smooth coefficients, respectively. The discontinuities of the coefficients are assumed to be given by manifolds of codime... View more
  • References (12)
    12 references, page 1 of 2

    [1] D. G. Aronson, Non-negarive solutions of linear parabolic equations, Ann. Scuola Norm. Sup. Pisa (3) 22 (1968), 607-694.

    [2] I. Babusˇka, B. Andersson, P. Smith and K. Levin, Damage analysis of fiber composites, Part I: Statisical analysis on fiber scale, Comput. Methods Appl. Mech. Engrg. 172 (1999), no. 1-4, 27-77.

    [3] M. Di Cristo and S. Vessella, Stable determination of the discontinuous conductivity coefficient of a parabolic equation, SIAM J. Math. Anal. 42 (2010), no. 1, 183-217.

    [4] E. B. Fabes and D. W. Stroock, A new proof of Moser's parabolic Harnack inequality using the old ideas of Nash, Arch. Rational Mech. Anal. 96 (1986), no. 4, 327-338.

    [5] A. Friedman, Partial differential equations, 2008, Dover Publications.

    [6] M. Ikehata, The enclosure method and its applications, Analytic extension formulas and their applications (Fukuoka, 1999/Kyoto, 2000) 87-103, Int. Soc. Anal. Appl. Comput. 9, Kluwer Acad. Publ., Dordrecht, 2001.

    [7] V. Isakov, K. Kim and G. Nakamura, Reconstruction of an unknown inclusion by thermography, to appear in Ann. Scuola Norm. Sup. Pisa.

    [8] O. A. Ladyzˇenskaja, V. Ya. Rivkind and N. N. Ural'ceva, The classical solvability of diffraction problems, Trudy Mat. Inst. Steklov 92 (1966), 116-146.

    [9] O. A. Ladyzˇenskaja, V. A. Solonnikov, N. N. Ural'ceva, Linear and quasilinear equations of parabolic type, Translated from the Russian by S. Smith, 1967, American Mathematical Society.

    [10] Y. Li and L. Nirenberg, Estimates for elliptic systems from composite material, Comm. Pure Appl. Math. 56 (2003), no. 7, 892-925.

  • Related Organizations (6)
  • Metrics
Share - Bookmark