East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
권호 표지
DOI QR코드

DOI QR Code

LOCAL CALDERÓN-ZYGMUND ESTIMATES FOR PARABOLIC EQUATIONS WITH DUAL DATA

  • Mikyoung, Lee (Department of Mathematics, Pusan National University)
  • Received : 2023.01.16
  • Accepted : 2023.01.21
  • Published : 2023.01.31
Download PDF
⟨ Previous Next ⟩

Abstract

We establish the interior Lq regularity estimates for spatial gradient of weak solutions to nonlinear parabolic equations with the inhomogeneity which is given by the divergence and nondivergence data.

Keywords

Acknowledgement

This work was supported by a 2-Year Research Grant of Pusan National University.

References

  1. E. Acerbi and G. Mingione: Gradient estimates for the p(x)-Laplacean system, J. Reine Angew. Math. 584 (2005), 117-148.
  2. E. Acerbi and G. Mingione: Gradient estimates for a class of parabolic systems, Duke Math. J. 136 (2007), no. 2, 285-320.
  3. V. Bogelein: Global Calderon-Zygmund theory for nonlinear parabolic systems, Calc. Var. Partial Differential Equations 51 (2014), no. 3-4, 555-596. https://doi.org/10.1007/s00526-013-0687-4
  4. S. Byun and W. Kim: Global Calderon-Zygmund estimate for p-Laplacian parabolic system, Math. Ann. 383 (2022), no. 1-2, 77-118. https://doi.org/10.1007/s00208-020-02089-z
  5. L. A. Caffarelli and I. Peral: On W1,p estimates for elliptic equations in divergence form, Comm. Pure Appl. Math. 51 (1998), no. 1, 1-21. https://doi.org/10.1002/(SICI)1097-0312(199801)51:1<1::AID-CPA1>3.0.CO;2-G
  6. F. Duzaar, F, G. Mingione, K. Steffen: Parabolic systems with polynomial growth and regularity, Mem. Amer. Math. Soc. 214 (2011), no. 1005, x+118 pp. https://doi.org/10.1090/S0065-9266-2011-00614-3
  7. E. DiBenedetto and J. Manfredi: On the higher integrability of the gradient of weak solutions of certain degenerate elliptic systems, Amer. J. Math. 115 (1993), no. 5, 1107-1134. https://doi.org/10.2307/2375066
  8. E. Giusti: Direct methods in the calculus of variations, World Scientific Publishing Co., Inc., River Edge, NJ, 2003.
  9. T. Iwaniec: Projections onto gradient fields and Lp-estimates for degenerated elliptic operators, Studia Math. 75 (1983), no. 3, 293-312. https://doi.org/10.4064/sm-75-3-293-312
  10. M. Lee and J. Ok: Local Calderon-Zygmund estimates for parabolic equations in weighted Lebesgue spaces, Math. Eng. 5 (2023), no. 3, Paper No. 062, 20 pp
  11. R.E. Showalter: Monotone operators in Banach space and nonlinear partial differential equations, Mathematical Surveys and Monographs 49, American Mathematical Society, Providence, RI, 1997.