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LOCAL CALDERO ́N-ZYGMUND ESTIMATES FOR PARABOLIC EQUATIONS WITH DUAL DATA

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영남수학회 (Youngnam Mathematical Society)|2023.01|East Asian Mathematical Journal|제39권 제1호|pp. 51-63

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키워드

parabolic equationweak solutionCaldero ́n-Zygmund estimateregularity theory.
주제분류수학

초록

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

Abstract

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

참고문헌 (11)

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  4. S. Byun, "Global Calder´on-Zygmund estimate for p-Laplacian parabolic system", Math. Ann, 383(1-2), pp.77~118 (2022)
  5. L. A. Caffarelli, "On W1,p estimates for elliptic equations in divergence form", Comm. Pure Appl. Math, 51(1), pp.1~21 (1998)
  6. F. Duzaar, "Parabolic systems with polynomial growth and regularity", Mem. Amer. Math. Soc, 214(1005), pp.x+118~ (2011)
  7. E. DiBenedetto, "On the higher integrability of the gradient of weak solutions of certain degenerate elliptic systems", Amer. J. Math, 115(5), pp.1107~1134 (1993)
  8. E. Giusti, "Direct methods in the calculus of variations" (2003), World Scientific Publishing Co., Inc
  9. T. Iwaniec, "Projections onto gradient fields and Lp-estimates for degenerated elliptic operators", Studia Math, 75(3), pp.293~312 (1983)
  10. M. Lee, "Local Calder´on-Zygmund estimates for parabolic equations in weighted Lebesgue spaces", Math. Eng, 5(3), pp.20~ (2023)
  11. R.E. Showalter, "Monotone operators in Banach space and nonlinear partial differential equations" (1997), American Mathematical Society

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