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A regularity theory for a general class of quasilinear elliptic partial differential equations and obstacle problems

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  1. H. J. Choe & J. Lewis, On the obstacle problem for quasilinear elliptic equation of p Laplacian type, to appear in SIAM J. Math. Analysis.

  2. E. DiBenedetto, C 1,α local regularity of weak solutions of degenerate elliptic equations, Nonlinear Anal. 7 (1983), 827–850.

    Google Scholar 

  3. M. Fuchs, Hölder continuity of the gradient for degenerate variational inequalities, Bonn Lecture Notes, 1989.

  4. M. Giaquinta, Multiple integrals in the Calculus of Variations and Non-linear Elliptic Systems, Annals of Math. Studies, Vol. 105, Princeton University Press, 1983.

  5. J. Lewis, Regularity of derivatives of solutions to certain degenerate elliptic equations, Indiana Univ. Math. J. 32 (1983), 849–858.

    Google Scholar 

  6. G. Lieberman, The natural generalization of the natural conditions of Ladyzhenskaya and Ural'tseva for elliptic equations, to appear in Comm. Partial Diff. Eqs.

  7. P. Lindquist, Regularity for the gradient of the solution to a nonlinear obstacle problem with degenerate ellipticity, Nonlinear Anal. 12 (1988), 1245–1255.

    Google Scholar 

  8. O. A. Ladyzhenskaya & N. N. Ural'tseva, Linear and Quasilinear Elliptic Equations, Academic Press, 1968.

  9. J. Manfredi, Regularity for minima of functionals with p-growth, J. Diff. Eqs. 76 (1988), 203–212.

    Google Scholar 

  10. J. Michael & W. Ziemer, Interior regularity for solutions to obstacle problems, Nonlinear Anal. 10 (1986), 1427–1448.

    Google Scholar 

  11. T. Norando, C 1,α local regularity for a class of quasilinear elliptic variational inequalities, Boll. Un. Ital. Mat. 5 (1986), 281–291.

    Google Scholar 

  12. J. Serrin, Local behavior of solutions of quasi-linear elliptic equations, Acta Math. 111 (1964), 247–302.

    Google Scholar 

  13. P. Tolksdorff, Regularity for a more general class of quasi-linear elliptic equations, J. Diff. Eqs. 51 (1984), 126–150.

    Google Scholar 

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

    Google Scholar 

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Communicated by J. Serrin

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Choe, H.J. A regularity theory for a general class of quasilinear elliptic partial differential equations and obstacle problems. Arch. Rational Mech. Anal. 114, 383–394 (1991).

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