Skip to main content
SpringerLink
Log in

The boundary value problems for non-linear elliptic equations and the maximum principle for Euler-Lagrange equations

  • Published:
Archive for Rational Mechanics and Analysis Aims and scope Submit manuscript

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. I. Bakelman, Generalized solutions of the Monge-Ampère equations, Dokl. Akad Nauk USSR, 111 (1957), 1143–1145.

    Google Scholar 

  2. I. Bakelman, Geometric methods of solution of elliptic equations, Monograph, Nauka, Moscow, (1965), 1–340.

    Google Scholar 

  3. I. Bakelman, R-curvature, estimates and stability of solutions for elliptic equations, Journal of Diff. Equations, 43, 1 (1982), 106–133.

    Google Scholar 

  4. I. Bakelman, The boundary value problems for N-dimensional Monge-Ampère equation; N-dimensional plasticity equation, IHES, Bures-sur-Yvette, (1984), preprint, 1–107.

    Google Scholar 

  5. A. D. Alexandrov. Existence and uniqueness of convex surface with prescribed integral curvature, Dokl. Akad. Nauk USSR, 35, 8. (1942), 143–147.

    Google Scholar 

  6. A. D. Alexandrov. Convex polyhedra, Monograph, Moscow-Leningrad (1950), 1–428.

  7. I. Bakelman, On the theory of Monge-Ampère equations, Vestnik LGU, N1, (1958), 25–38.

    Google Scholar 

  8. I. Bakelman, A. Werner, & B. Kantor, Introduction to global differential geometry, Monograph, Nauka, Moscow, (1973), 1–440.

    Google Scholar 

  9. H. Busemann, Convex surfaces, Monograph, Interscience Publishers, Inc., NewYork, (1958), 1–238.

    Google Scholar 

  10. A. Alexandrov, Intrinsic geometry of convex surfaces, Monograph, Moscow-Leningrad (1948), 1–427.

    Google Scholar 

  11. A. Pogorelov, Exterior geometry of convex surfaces, Monograph, Moscow, Nauka, (1969), 1–759; Engl. transl. Transl. Math. Monographs, v. 35, Amer. Math. Soc. 1973.

    Google Scholar 

  12. S. N. Bernstein, Collection of papers, vol. 3, Akad. Nauk of USSR, (1960), 1–439.

  13. O. A. Ladyzhenskya & N. N. Uraltzeva, Linear and quasilinear elliptic equations, Nauka, (1973), 2nd ed., 1–576.

  14. D. Gilbarg & N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, (monograph), Second Edition, Springer Verlag, (1983), 1–511.

  15. I. Bakelman, Geometric problems in quasilinear elliptic equations, Uspekhi Mathem. Nauk, 25: 3, (1970), 42–112; Russian Mathem. Surveys (1970), 25, N∘ 3, 45–109.

    Google Scholar 

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

  17. I. Bakelman, Notes concerning the torsion problem of hardening rods, IMA Preprint Series, (1986), 1–38.

  18. Ch. Morrey, Multiple integrals, Monograph. Springer Verlag (1966).

  19. M. Protter & H. F. Weinberger, Maximum principles in Differential equations. Monograph, Prentice-Hall, Inc, (1967), 1–261.

  20. L. Caffarelli, L. Nirenberg, & J. Spruck, The Dirichlet problem for Non-linear Second Order Elliptic Equations I. Monge-Ampère equations, Comm. pure and Appl. Mathematics, (1984).

  21. S. Y. Cheng & S. T. Yau, On the regularity of the solution of the Monge-Ampère equations det (uij) = F(x, u). Comm. pure and Appl. Mathem., 29, (1976), 495–516.

    Google Scholar 

  22. A. V. Pogorelov, The Minkowski multidimensional problem, New York, J. Wiley, (1978).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Texas A. & M. University, College Station

    Ilya J. Bakelman

Authors
  1. Ilya J. Bakelman
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Dedicated to James Serrin on his sixtieth birthday

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bakelman, I.J. The boundary value problems for non-linear elliptic equations and the maximum principle for Euler-Lagrange equations. Arch. Rational Mech. Anal. 93, 271–300 (1986). https://doi.org/10.1007/BF00281501

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00281501

Keywords

Search

Navigation