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Published Works of James Serrin Published Works of James Serrin Bibliographic information at the end of an entry is enclosed in brackets when it refers to the full volume cited by the entry. 1. Free boundaries and jets in the theory of cavitation (with DAVID GILBARG). Journal of Mathematics and Physics 29 (1950), pp. 1-12. 2. Uniqueness theorems for two free boundary problems. American Journal of Mathe­ matics 74 (1952), pp.492-506. 3. Existence theorems for some hydrodynamical free boundary problems. Journal of Rational Mechanics and Analysis 1 (1952), pp. 1-48. 4. Two hydrodynamical comparison theorems. Journal of Rational Mechanics and Analysis 1 (1952), pp. 563-572. 5. On plane and axially symmetric free boundary problems. Journal of Rational Me­ chanics and Analysis 2 (1953), pp. 563-575. 6. A note on the wave equation. Proceedings of the American Mathematical Society 5 (1954), pp. 307-308. 7. Comparison theorems for subsonic flows. Journal of Mathematics and Physics 33 (1954), pp.27-45. 8. On the Phragmen-Lindel6f theorem for elliptic partial differential equations. Journal of Rational Mechanics and Analysis 3 (1954), pp.395--413. 9. A uniqueness theorem for the parabolic equation ut = a(x) uxx + hex) Ux + c(x) u. Bulletin of the American Mathematical Society 60 (1954), p.344. Abstract, only published version. 10. Uniqueness of axially symmetric subsonic flow past a finite body (with DAVID GILBARG). Journal of Rational Mechanics and Analysis 4 (1955), pp. 169-175. 11. A characterization of regular boundary points for second order linear differential equations. Bulletin of the American Mathematical Society 61 (1955), p. 224. [Ab­ stract, only published version.] 12. On the Harnack inequality for linear elliptic equations. Journal d'Anaiyse Mathe­ matique 4 (1956), pp. 292-308. 13. On isolated singularities of solutions of second order linear elliptic equations (with DAVID GILBARG). Journal d'Analyse Mathematique 4 (1956), pp.309-340. 820 J. SERRIN 14. A note on harmonic functions defined in a half-plane. Duke Mathematical Journal 24 (1956), pp. 523-526. 15. On the HOlder continuity of quasi-conformal and elliptic mappings (with ROBERT FINN). Transactions of the American Mathematical Society 89 (1958), pp. 1-15. 16. Mathematical principles of classical fluid mechanics. Handbuch der Physik, vol. VIIIll (1959), pp. 125-263. 16A. Russian Translation: Foreign Literature Publishing House, Moscow 1963 (256 pages). 17. On the stability of viscous fluid motions. Archive for Rational Mechanics and Anal­ ysis 3 (1959), pp. 1-13. 18. A note on the existence of periodic solutions of the Navier-Stokes equations. Archive for Rational Mechanics and Analysis 3 (1959), pp. 120-122. 19. On the uniqueness of compressible fluid motions. Archive for Rational Mechanics and Analysis 3 (1959), pp.271-288. 20. On the derivation of stress-deformation relations for a Stokesian fluid. Journal of Mathematics and Mechanics 8 (1959), pp.459-470. 21. Poiseuille and Couette flow of non-Newtonian fluids. Zeitschrift fur Angewandte Mathematik und Mechanik 39 (1959), pp.295-299. 22. On a fundamental theorem of the calculus of variations. Acta Mathematica 102 (1959), pp. 1-22. 23. A new definition of the integral for non-parametric problems in the calculus of variations. Acta Mathematica 102 (1959), pp.23-32. 24. The exterior Dirichlet problem for second order elliptic equations (with NORMAN MEYERS). Journal of Mathematics and Mechanics 9 (1960), pp.513-538. 25. On the area of curved surfaces. American Mathematical Monthly 68 (1961), pp. 435- 440. 26. On the differentiability of functions of several variables. Archive for Rational Mechanics and Analysis 7 (1961), pp.359-372. 27. On the definition and properties of certain variational integrals. Transactions of the American Mathematical Society 101 (1961), pp. 139-167. 28. On the entropy change through a shock layer (with Y. C. WHANG). Journal of the Aerospace Sciences 28 (1961), pp.990-991. 29. Dirichlet's principle in the calculus of variations. Proceedings of Symposia in Pure Mathematics (American Mathematical Society) IV, pp. 17-22. 30. Interior estimates for solutions of the Navier-Stokes equations. Partial Differential Equations and Continuum Mechanics, edited by R. LANGER, pp. 376-378. University of Wisconsin Press, Madison 1961. [Conference proceedings.] 31. On the interior regularity of weak solutions of the Navier-Stokes equations. Ar­ chive for Rational Mechanics and Analysis 9 (1962), pp. 187-195. 32. Strong convergence in a product space. Proceedings of the American Mathematical Society 13 (1962), pp.651-655. 33. The initial value problem for the Navier-Stokes equations. Nonlinear problems, edited by R. E. LANGER, pp. 69-98. University of Wisconsin Press, Madison 1963. [Conference proceedings.] 34. Variational problems of minimal surface type, I (with HOWARD JENKINS). Archive for Rational Mechanics and Analysis 12 (1963), pp. 185-212. See also entries 47 and 57. 35. Comparison and averaging methods in mathematical physics. Proprieta di Media e Teoremi di Confronto in Fisica Matematica, pp. 1-87. Centro Internazionale Matematico Estivo, Rome 1963. 36. A priori estimates for solutions of the minimal surface equation. Archive for Ration­ al Mechanics and Analysis 14 (1963), pp. 376-383. See also entry 54. Published Works 821 37. A Harnack inequality for nonlinear equations. Bulletin of the American Mathemati­ cal Society 69 (1963), pp.481-486. See also entries 38 and 44. 38. Local behavior of solutions of quasi-linear equations. Acta Mathematica 111 (1964), pp.247-302. 39. Sublinear functions of measures and variational integrals (with CASPAR GOFFMAN). Duke Mathematical Journal 31 (1964), pp. 159-178. 40. H = W (with NORMAN MEYERS). Proceedings of the National Academy of Sciences (USA) 51 (1964), pp. 1055-1056. 41. Removable singularities of solutions of elliptic equations. Archive for Rational Mechanics and Analysis 17 (1964), pp.67-78. See also entry 45. 42. Pathological solutions of elliptic differential equations. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (Serie II) 18 (1964), pp.385-387. 43. Singularities of solutions of nonlinear equations. Proceedings of Symposia in Applied Mathematics (American Mathematical Society) XVII (1965), pp.68-88. 44. Isolated singularities of solutions of quasi-linear equations. Acta Mathematica 113 (1965), pp.219-240. 45. Removable singularities of solutions of elliptic differential equations, II. Archive for Rational Mechanics and Analysis 20 (1965), pp. 163-169. 46. The Dirichlet problem for the minimal surface equation, with infinite data (with HOWARD JENKINS). Bulletin of the American Mathematical Society 72 (1966), pp. 102-106. See also entry 57. 47. Variational problems of minimal surface type, II: Boundary value problems for the minimal surface equation (with HOWARD JENKINS). Archive for Rational Mechan­ ics and Analysis 21 (1966), pp.321-342. 48. Isolated singularities of solutions of linear elliptic equations (with H. F. WEIN­ BERGER). American Journal of Mathematics 88 (1966), pp.258-272. 49. Removable singularities of solutions of elliptic equations. Notices of the American Mathematical Society 13 (1966), pp. 123. Abstract, only published version. 50. Local behavior of solutions of quasilinear parabolic equations (with D. G. ARON­ SON). Archive for Rational Mechanics and Analysis 25 (1967), pp.81-122. 51. A maximum principle for nonlinear parabolic equations (with D. G. ARONSON). Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (Serie II) 21 (1967), pp.291-305. 52. The Dirichlet problem for quasilinear elliptic equations with many independent variables. Proceedings of the National Academy of Sciences (USA) 58 (1967), pp. 1829-1835. See also entry 62. 53. On the asymptotic behavior of velocity profiles in the Prandtl boundary layer theory. Proceedings of the Royal Society of London, A 299 (1967), pp.491-507. 54. Addendum to "A priori estimates for solutions of the minimal surface equation". Archive for Rational Mechanics and Analysis 28 (1968), pp. 149-154. See also entry 36. 55. The Dirichlet problem for the minimal' surface equation in higher dimensions. Journal fiir die reine und angewandte Mathematik 223 (1968), pp. 170-187. 56. On the mathematical basis of Prandtl's boundary layer theory: an example. Ar­ chive for Rational Mechanics and Analysis 28 (1968), pp.217-225. 57. Variational problems of minimal surface type, III: The Dirichlet problem with in­ finite data (with HOWARD JENKINS). Archive for Rational Mechanics and Analysis 29 (1968), pp. 304-322. 58. The behavior of similar solutions in a compressible boundary layer (with J. B. Mc­ LEOD). Journal of Fluid Mechanics 34 (1968), pp.337-342. 59. A new proof in differentiation theory. Notices of the American Mathematical Society 15 (1968), p. 1036. Abstract; see also RUDIN, W.: Real and Complex Analysis, Second Edition (McGraw-Hill, 1974), pp. xii and 435, and pp.162-167. 822 J. SERRIN 60. A general chain rule for derivatives (with D. E. VARBERG). American Mathematical Monthly 76 (1969), pp.514-520. 61. The existence of similar solutions for some laminar boundary layer problems (with J. B. McLEOD). Archive for Rational Mechanics and Analysis 31 (1969), pp. 288- 303. 62. The problem of Dirichlet for quasilinear elliptic differential equations with many independent variables. Philosophical Transactions of the Royal Society of London, A 264 (1969), pp.4l3-496. 62A. The Dirichlet problem for nonuniformly elliptic partial differential equations. Notices of the American Mathematical Society 14, (1967) p. 712. 62B. On the nonexistence of solutions of Dirichlet's problem. Notices of the American Mathematical Society 14 (1967), p.841. 63. On surfaces of constant mean curvature which span a given space curve. Mathe­ matische Zeitschri/t 88 (1969), pp. 77-88. 64. Existence theorems for more compressible boundary layer problems. Studies in Applied Mathematics (SIAM) 5 (1970), pp. 35-42. [Conference proceedings.] 65. The Dirichlet problem for surfaces of constant mean curvature. Proceedings of the London Mathematical Society (3) 21 (1970), pp.361-384. 66. On the strong maximum principle for nonlinear second order differential inequali­ ties.
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