Advertisement

Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Properties of overdetermined first order elliptic systems

This is a preview of subscription content, log in to check access.

Bibliography

  1. 1.

    Adams, J.F., Lax, P.D., & Phillips, R.S., On matrices whose real linear combinations are nonsingular. Proc. Amer. Math. Soc., 16, 318–322 (1965).

  2. 2.

    Courant, R., & Hilbert, D., Methods of Mathematical Physics. Vol. II, Interscience Publishers, New York 1962.

  3. 3.

    Douglis, A., & Nirenberg, L., Interior estimates for elliptic systems of partial differential equations. Comm. Pure Appl. Math., vol. VIII 503–538 (1955).

  4. 4.

    Geramita, A.V., & Pullman, N.J., A theorem of Hurwitz and Radon and orthogonal projective modules. Proc. Amer. Math. Soc., 42, 51–56 (1974).

  5. 5.

    Hile, G.N., & Protter, M.H., Maximum principles for a class of first order elliptic systems. J. Differential Equations, 24, 136–151 (1977).

  6. 6.

    Hile, G.N., & Protter, M.H., Unique Continuation and the Cauchy problem for first order systems of partial differential equations. Comm. in Partial Differential Equations, 1, 437–465 (1976).

  7. 7.

    Hörmander, L., Partial Differential Operators. Springer-Verlag, New York 1965.

  8. 8.

    Lam, T.Y., The Algebraic Theory of Quadratic Forms. W.A. Benjamin and Co. 1973.

  9. 9.

    Newman, M.H.A., Note on an algebraic theorem of Eddington. J. London Math. Soc., 7, 93–99 (1932).

  10. 10.

    Nirenberg, L., Uniqueness in Cauchy problems for differential equations with constant leading coefficients. Comm. Pure Appl. Math., 10, 89–105 (1957).

Download references

Author information

Additional information

Dr. Hile was supported in part by grant MCS 76-07180 of the National Science Foundation.

Communicated by J. Serrin

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Hile, G.N., Protter, M.H. Properties of overdetermined first order elliptic systems. Arch. Rational Mech. Anal. 66, 267–293 (1977). https://doi.org/10.1007/BF00250674

Download citation

Keywords

  • Neural Network
  • Complex System
  • Nonlinear Dynamics
  • Electromagnetism
  • Elliptic System