Pacific Journal of Mathematics

Closed extensions of the Laplace operator determined by a general class of boundary conditions.

W. G. Bade and R. S. Freeman

Article information

Source
Pacific J. Math., Volume 12, Number 2 (1962), 395-410.

Dates
First available in Project Euclid: 14 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1103036479

Mathematical Reviews number (MathSciNet)
MR0165132

Zentralblatt MATH identifier
0198.17403

Subjects
Primary: 35.45
Secondary: 31.20

Citation

Bade, W. G.; Freeman, R. S. Closed extensions of the Laplace operator determined by a general class of boundary conditions. Pacific J. Math. 12 (1962), no. 2, 395--410. https://projecteuclid.org/euclid.pjm/1103036479


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References

  • [1] N. Aronszajn and K. T. Smith, Functional spaces and functional completion, Ann. Inst. Fourier, Grenoble, 6 (1955-56), 125-185.
  • [2] F. E. Browder, On the regularity properties of solutions of elliptic differential equations, Comm. on Pure and Applied Math., 9 (1956), 351-361.
  • [3] F. E. Browder, On the spectral theory of strongly elliptic differential operators, Proc. Nat. Acad. Sci., 45 (1959), 1423-1431.
  • [4] A. P. Calderon and A. Zygmund, On the existence of certain singular integrals,Acta Math., 88 (1952), 85-139.
  • [5] J. W. Calkin, Abstract self-adjoint boundary conditions, Proc. Nat. Acad. Sci., 24 (1938), 38-42.
  • [6] J. W. Calkin, Abstract symmetric boundary conditions, Trans. Amer. Math. Soc, 45 (1939), 369-442.
  • [7] J. W. Calkin, General self-adjointboundary conditions for certain partialdifferential operators, Proc. Nat. Acad. Sci., 25 (1939), 201-206.
  • [8] J. W. Calkin, Abstract definite boundary value problems, ibid., 26 (1940), 708-712.
  • [5] N. Dunford and J. T. Schwartz, Linear Operators, Part I: General theory, New York, 1958.
  • [10] G. Ehrling, On a type of eigenvalue problem for certain elliptic differentialoperators, Math. Scand., 2 (1954) 267-285.
  • [11] P. Frank and R. von Mises, Die Differentialand Integralgleichungender Mechanik und Physik, vol. 1, Braunschweig, 1930.
  • [12] R. S. Freeman, Self-adjoint boundary conditions for the Laplace operator, Thesis, University of California, Berkeley, 1959.
  • [13] R. S. Freeman, Closed extensions of the Laplace operator determined by a general class of boundary conditions for unbounded regions, to appear.
  • [14] K. O. Friedrichs, Spektraltheorie halbbeschrankter Operatoren und Anwendungauf die Spektralzerlegung von DifferentialoperatorenI, II, Math. Ann., 109 (1934), 465-486, 685-713.
  • [15] J. T. Joichi, On closed operators with closed range, Proc. Amer. Math. Soc, 11 (1960), 80-83.
  • [16] O. D. Kellogg, Foundations of potential theory, Springer, Berlin, 1929.
  • [17] P. Lax and A. Milgram, Parabolic equations, Ann. of Math. Studies No. 33, Princeton, 1954.
  • [18] K. R. Lucas, Submanifoldsof dimension n --1 in En with normals satisfying a Lipschitz condition, Studies in eigenvalue problems, Technical Report 18, University of Kansas, 1957.
  • [19] C. B. Morrey, Jr., Functions of several variables and absolute continuityII, Duke Math. J., 6 (1940), 186-215.
  • [20] J. Odhnoff, Operators generated by differentialproblems with eigenvalueparameter in equation and boundary condition, Thesis, Lund University, 1959.
  • [21] J. W. Smith, Two classes of self-adjoint boundary conditions for the Laplacian operator, Thesis, University of California, Berkeley, 1950.
  • [22] W. J. Sternberg and T. L. Smith, The theory of potential and sphericalharmonics, Toronto, 1944.