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Behavior at the boundary of solutions of quasilinear elliptic equations

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References

  1. Bagby, T., Quasitopologies and rational approximation. J. Functional Analysis 10, 259–268 (1972).

    Google Scholar 

  2. Calderon, A. P., Lebesgue spaces of differentiable functions and distributions. Proc. Symp. Pure Math., Vol. 4, 33–49, Amer. Math. Soc., Providence, R.I. 1961.

    Google Scholar 

  3. DeGiorgi, E., Sulla differenziabilità e l'analiticità delle estremali degli integrali multipli regolari. Mem. Accad. Sci. Torino (3a) 3, 25–43 (1957).

    Google Scholar 

  4. Federer, H., & W. P. Ziemer, The Lebesgue set of a function whose distribution derivatives are pth power integrable. Ind. Univ. Math. J. 22, 139–158 (1972).

    Google Scholar 

  5. Ladyzhenskaya, O. A., & N. N. Ural'tseva, Linear and Quasilinear Elliptic Equations. New York: Academic Press 1968.

    Google Scholar 

  6. Meyers, N. G., A theory of capacities for potentials of functions in Lebesgue classes. Math. Scand 26, 255–292 (1970).

    Google Scholar 

  7. Moser, J., A new proof of DeGiorgi's theorem concerning the regularity problem for elliptic differential equations. Comm. Pure and Applied Math. 13, 457–468 (1960).

    Google Scholar 

  8. Polking, J., Approximation in L pby solutions of elliptic partial differential equations (to appear).

  9. Serrin, J., Local behavior of solutions of quasilinear equations. Acta. Math. 111, 302–347 (1964).

    Google Scholar 

  10. Stein, E., Singular Integrals and Differentiability Properties of Functions. Princeton University Press 1970.

  11. Trudinger, N., On Harnack type inequalities and their applications to quasilinear equations. Comm. Pure and Appl. Math. 20, 721–747 (1967).

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Kentucky, Lexington

    Ronald Gariepy & William P. Ziemer

  2. Department of Mathematics, Indiana University, Bloomington, Indiana

    Ronald Gariepy & William P. Ziemer

Authors
  1. Ronald Gariepy
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  2. William P. Ziemer
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Communicated by J. Serrin

Research supported in part by a grant from the National Science Foundation.

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Gariepy, R., Ziemer, W.P. Behavior at the boundary of solutions of quasilinear elliptic equations. Arch. Rational Mech. Anal. 56, 372–384 (1974). https://doi.org/10.1007/BF00248149

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  • DOI: https://doi.org/10.1007/BF00248149

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