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Second Order Regularity for the A-Laplace Operator

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Abstract

In this paper we establish second order regularity for the quasilinear elliptic equation Δ A u =  f, where Δ A is the so called A-Laplace operator.

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References

  1. S. Challal and A. Lyaghfouri : Hölder Continuity of Solutions to the A-Laplace Equation Involving Measures. Communications in Pure and Applied Analysis. Vol. 8, No. 5, 1577-1583 (2009).

  2. Giusti E.: Direct methods in the calculus of variations. World Scientific Publishing Co., Inc., River Edge, NJ (2003)

    Book  MATH  Google Scholar 

  3. G. M. Lieberman : The natural generalization of the natural conditions of Ladyzhenskaya and Uraltseva for elliptic equations. Comm. Partial Differential Equations Vol. 16, No. 2-3, 311-361 (1991).

  4. O. Ladyženskaya and N. Ural’ceva : Linear and quasilinear elliptic equations. Academic Press, New York, 1968 (second Russian edition, Nauka 1973).

  5. P. Lindqvist : Notes on the p-Laplace equation. Report. University of Jyväskylä, Department of Mathematics and Statistics, 102, 2006.

  6. W. B. Liu and J. W. Barrett : A remark on the regularity of the solutions of the p-Laplacian and its application to their finite element approximation. J. Math. Anal. Appl. Vol. 178, No. 2, 470-487 (1993).

  7. P. Tolksdorf : Regularity for a more general class of quasilinear elliptic equations. J. Differential Equations, Vol. 51, No. 1, 126-150 (1984).

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Authors and Affiliations

  1. Fields Institute, 222 College Street, Toronto, M5T 3J1, Canada

    Samia Challal & Abdeslem Lyaghfouri

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  1. Samia Challal
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  2. Abdeslem Lyaghfouri
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Correspondence to Abdeslem Lyaghfouri.

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Challal, S., Lyaghfouri, A. Second Order Regularity for the A-Laplace Operator. Mediterr. J. Math. 7, 283–296 (2010). https://doi.org/10.1007/s00009-010-0053-0

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  • DOI: https://doi.org/10.1007/s00009-010-0053-0

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