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Exponential decay estimates for a class of nonlinear Dirichlet problems

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References

  1. Toupin, R. A., Saint-Venant's principle. Arch. Rational Mech. Anal. 18, 83–96 (1965).

    Article  MATH  MathSciNet  Google Scholar 

  2. Knowles, J. K., On Saint-Venant's principle in the two-dimensional linear theory of elasticity. Arch. Rational Mech. Anal. 21, 1–22 (1966).

    Article  MathSciNet  Google Scholar 

  3. Horgan, C. O., & L. T. Wheeler, Exponential decay estimates for second-order quasilinear elliptic equations. J. Math. Anal. Appl. 59, 267–277 (1977).

    Article  MathSciNet  Google Scholar 

  4. Wheeler, L. T., & C. O. Horgan, A two-dimensional Saint-Venant principle for second-order linear elliptic equations. Quart. Appl. Math. 34, 257–270 (1976).

    MathSciNet  Google Scholar 

  5. Horgan, C. O., & L. T. Wheeler, Maximum principles and pointwise error estimates for torsion of shells of revolution. J. Elasticity 7, 387–410 (1977).

    Google Scholar 

  6. Horgan, C. O., and L. T. Wheeler, Spatial decay estimates for the heat equation via the maximum principle. Z. Angew. Math. Phys. 27, 371–376 (1976).

    MathSciNet  Google Scholar 

  7. Roseman, J. J., The principle of Saint-Venant in linear and non-linear plane elasticity. Arch. Rational Mech. Anal. 26, 142–162 (1967).

    MATH  MathSciNet  Google Scholar 

  8. Breuer, S., & J. J. Roseman, On Saint-Venant's principle in three-dimensional nonlinear elasticity. Arch. Rational Mech. Anal. 62, 191–203 (1977).

    Google Scholar 

  9. Roseman, J. J., Phragmén-Lindelöf theorems for some nonlinear elliptic partial differential equations. J. Math. Anal. Appl. 43, 587–602 (1973).

    Article  MATH  MathSciNet  Google Scholar 

  10. Roseman, J. J., The rate of decay of a minimal surface defined over a semi-infinite strip. J. Math. Anal. Appl. 46, 545–554 (1974).

    Article  MATH  MathSciNet  Google Scholar 

  11. Knowles, J. K., A note on the spatial decay of a minimal surface over a semi-infinite strip. J. Math. Anal. Appl. 59, 29–32 (1977).

    Article  MATH  MathSciNet  Google Scholar 

  12. Serrin, J., The problem of Dirichlet for quasilinear elliptic differential equations with many independent variables. Phil. Trans. Roy. Soc. Lond. 264, 413–496 (1969).

    ADS  MATH  MathSciNet  Google Scholar 

  13. Rabinowitz, P.H., Variational methods for nonlinear elliptic eigenvalue problems. Indiana Univ. Math. J. 23, 729–754 (1974).

    Article  MATH  MathSciNet  Google Scholar 

  14. Knowles, J. K., A Saint-Venant principle for a class of second-order elliptic boundary value problems. Z. Angew. Math. Phys. 18, 473–490 (1967).

    MATH  Google Scholar 

  15. Horgan, C. O., & L. T. Wheeler, Spatial decay estimates for the Navier-Stokes equations with application to the problem of entry flow. SIAM J. Appl. Math. 35, 97–116 (1978).

    Article  ADS  MathSciNet  Google Scholar 

  16. Horgan, C. O., Plane entry flows and energy estimates for the Navier-Stokes equations. Arch. Rational Mech. Anal. 68, 359–381 (1978).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  17. Friedman, A., Partial Differential Equations, Reprinted by R.E. Krieger Publishing Co., New York, 1976.

    Google Scholar 

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Communicated by G. Strang

The work of Professor C.O. Horgan was supported by the National Science Foundation under Grants ENG 75-13643 and ENG 78-26071. The work of Professor W.E. OLMSTEAD was supported by the National Science Foundation under Grant MCS 77-01327.

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Horgan, C.O., Olmstead, W.E. Exponential decay estimates for a class of nonlinear Dirichlet problems. Arch. Rational Mech. Anal. 71, 221–235 (1979). https://doi.org/10.1007/BF00280597

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