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A new proof of L p estimates for the parabolic polyharmonic equations

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Abstract

In this paper we obtain local L p estimates for the parabolic polyharmonic equations by a straightforward approach.

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References

  1. Chen Y. Parabolic Partial Differential Equations of Second Order (in Chinese). Beijing: Peking University Press, 2003

    Google Scholar 

  2. DiBenedetto E. Partial Differential Equations. Boston-Basel-Berlin: Birkhäuser, 1995

    MATH  Google Scholar 

  3. Ladyzenskaja O A, Solonnikov V A, Uralceva N N. Linear and Quasilinear Equations of Parabolic Type. Providence, RI: American Mathematical Society, 1968

    Google Scholar 

  4. Lieberman G M. Second Order Parabolic Differential Equations. River Edge, NJ: World Scientific Publishing Company, 1996

    MATH  Google Scholar 

  5. Wang L. A geometric approach to the Calderón-Zygmund estimates. Acta Math Sin (Engl Ser), 19(2): 381–396 (2003)

    Article  MathSciNet  Google Scholar 

  6. Caffarelli L A, Peral I. On W 1,p estimates for elliptic equations in divergence form. Comm Pure Appl Math, 51(1): 1–21 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  7. Solonnikov V A. On boundary value problems for linear parabolic systems of differential equations of general form. Trudy Mat Inst Steklov, 83: 3–63 (1965)

    MathSciNet  Google Scholar 

  8. Acerbi E, Mingione G. Gradient estimates for a class of parabolic systems. Duke Math J, 136: 285–320 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  9. Evans L C. Partial Differential Equations. Graduates Studies in Mathematics, Vol. 19. Providence, RI: American Mathematical Society, 1998

    Google Scholar 

  10. Chen Y, Wu L. Second Order Elliptic Partial Differential Equations and Elliptic Systems. Providence, RI: American Mathematical Society, 1998

    Google Scholar 

  11. Giquinta. M. Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. Princeton, NJ: Princeton University Press, 1983

    Google Scholar 

  12. Adams R A, Fournier J J F. Sobolev Spaces. 2nd ed. New York: Academic Press, 2003

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, 200444, China

    FengPing Yao

  2. LMAM, School of Mathematical Sciences, Peking University, Beijing, 100871, China

    ShuLin Zhou

Authors
  1. FengPing Yao
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  2. ShuLin Zhou
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Corresponding author

Correspondence to FengPing Yao.

Additional information

Yao was supported by the Innovation Foundation of Shanghai University (Grant No. A10-0101-08-905), Shanghai Leading Academic Discipline Project (Grant No. J50101) and Key Disciplines of Shanghai Municipality (Grant No. S30104). Zhou was supported by the National Basic Research Program of China (Grant No. 2006CB705700), National Natural Science Foundation of China (Grant No. 60532080), and the Key Project of Chinese Ministry of Education (Grant No. 306017)

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Yao, F., Zhou, S. A new proof of L p estimates for the parabolic polyharmonic equations. Sci. China Ser. A-Math. 52, 749–756 (2009). https://doi.org/10.1007/s11425-009-0048-0

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  • DOI: https://doi.org/10.1007/s11425-009-0048-0

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