Quadratic variational theory and linear elliptic partial differential equations
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- by Magnus R. Hestenes
- Trans. Amer. Math. Soc. 101 (1961), 306-350
- DOI: https://doi.org/10.1090/S0002-9947-1961-0133575-0
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References
- N. Aronszajn, On coercive integro-differential quadratic forms, Conference on Partial Differential Equations, University of Kansas, 1954, Technical Report No. 14, pp. 94-106.
- Felix E. Browder, On the regularity properties of solutions of elliptic differential equations, Comm. Pure Appl. Math. 9 (1956), 351–361. MR 90740, DOI 10.1002/cpa.3160090307
- Felix E. Browder, Eigenfunction expansions for nonsymmetric partial differential operators. II, Amer. J. Math. 81 (1959), 1–22. MR 107094, DOI 10.2307/2372847
- Felix E. Browder, Estimates and existence theorems for elliptic boundary value problems, Proc. Nat. Acad. Sci. U.S.A. 45 (1959), 365–372. MR 132913, DOI 10.1073/pnas.45.3.365
- J. W. Calkin, Functions of several variables and absolute continuity. I, Duke Math. J. 6 (1940), 170–186. MR 1278 R. Dennemeyer, Quadratic forms in Hilbert space and second order elliptic differential equations, Ph.D. Dissertation, University of California, Los Angeles, 1956, 108 pp.
- K. O. Friedrichs, On the differentiability of the solutions of linear elliptic differential equations, Comm. Pure Appl. Math. 6 (1953), 299–326. MR 58828, DOI 10.1002/cpa.3160060301
- Lars Gårding, Dirichlet’s problem for linear elliptic partial differential equations, Math. Scand. 1 (1953), 55–72. MR 64979, DOI 10.7146/math.scand.a-10364
- Lawrence M. Graves, The Weierstrass condition for multiple integral variation problems, Duke Math. J. 5 (1939), 656–660. MR 99 L. Hörmander, On the theory of general partial differential operators, Acta Math. vol. 94 (1955) pp. 161-284.
- Magnus R. Hestenes, Applications of the theory of quadratic forms in Hilbert space to the calculus of variations, Pacific J. Math. 1 (1951), 525–581. MR 46590
- Magnus R. Hestenes, Sufficient conditions for multiple integral problems in the calculus of variations, Amer. J. Math. 70 (1948), 239–276. MR 25091, DOI 10.2307/2372325
- Fritz John, Derivatives of continuous weak solutions of linear elliptic equations, Comm. Pure Appl. Math. 6 (1953), 327–335. MR 58829, DOI 10.1002/cpa.3160060302
- Peter D. Lax, On Cauchy’s problem for hyperbolic equations and the differentiability of solutions of elliptic equations, Comm. Pure Appl. Math. 8 (1955), 615–633. MR 78558, DOI 10.1002/cpa.3160080411
- C. B. Morrey Jr., Functions of several variables and absolute continuity, II, Duke Math. J. 6 (1940), 187–215. MR 1279 —, Multiple integral problems in the calculus of variations, University of California Publications in Mathematics, New Series, vol. 1 (1943).
- C. B. Morrey Jr., Second-order elliptic systems of differential equations, Contributions to the theory of partial differential equations, Annals of Mathematics Studies, no. 33, Princeton University Press, Princeton, N.J., 1954, pp. 101–159. MR 0068091
- Louis Nirenberg, Remarks on strongly elliptic partial differential equations, Comm. Pure Appl. Math. 8 (1955), 649–675. MR 75415, DOI 10.1002/cpa.3160080414
- Martin Schechter, On estimating elliptic partial differential operators in the $L_2$ norm, Amer. J. Math. 79 (1957), 431–443. MR 88648, DOI 10.2307/2372690
- Martin Schechter, Coerciveness of linear partial differential operators for functions satisfying zero Dirichlet-type boundary data, Comm. Pure Appl. Math. 11 (1958), 153–174. MR 132911, DOI 10.1002/cpa.3160110202
- Martin Schechter, Solution of the Dirichlet problem for equations not necessarily strongly elliptic, Bull. Amer. Math. Soc. 64 (1958), 371–372. MR 171071, DOI 10.1090/S0002-9904-1958-10239-6
- Martin Schechter, Integral inequalities for partial differential operators and functions satisfying general boundary conditions, Comm. Pure Appl. Math. 12 (1959), 37–66. MR 141879, DOI 10.1002/cpa.3160120104
- Martin Schechter, General boundary value problems for elliptic partial differential equations, Bull. Amer. Math. Soc. 65 (1959), 70–72. MR 104910, DOI 10.1090/S0002-9904-1959-10279-2 L. van Hove, Sur l’extension de la condition de Legendre du calcul des variations aux intégrales multiples à plusieurs fonctions inconnues, Nederl. Akad. Wetensch. Indag. Math. vol. 9 (1947) pp. 3-8.
Bibliographic Information
- © Copyright 1961 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 101 (1961), 306-350
- MSC: Primary 35.04; Secondary 35.43
- DOI: https://doi.org/10.1090/S0002-9947-1961-0133575-0
- MathSciNet review: 0133575