A Fatou theorem for the general one-dimensional parabolic equation
HTML articles powered by AMS MathViewer
- by Stanley Sawyer PDF
- Bull. Amer. Math. Soc. 79 (1973), 1210-1215
References
- D. G. Aronson, Uniqueness of positive weak solutions of second order parabolic equations, Ann. Polon. Math. 16 (1965), 285–303. MR 176231, DOI 10.4064/ap-16-3-285-303
- D. G. Aronson and P. Besala, Uniqueness of positive solutions of parabolic equations with unbounded coefficients, Colloq. Math. 18 (1967), 125–135. MR 219900, DOI 10.4064/cm-18-1-125-135
- Leo Breiman, Probability, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1968. MR 0229267
- William Feller, The parabolic differential equations and the associated semi-groups of transformations, Ann. of Math. (2) 55 (1952), 468–519. MR 47886, DOI 10.2307/1969644
- William Feller, On second order differential operators, Ann. of Math. (2) 61 (1955), 90–105. MR 68082, DOI 10.2307/1969621
- Avner Friedman, On the uniqueness of the Cauchy problem for parabolic equations, Amer. J. Math. 81 (1959), 503–511. MR 104907, DOI 10.2307/2372754
- Avner Friedman, Uniqueness for the Cauchy problem for degenerate parabolic equations, Pacific J. Math. 46 (1973), 131–147. MR 330773
- Philip Hartman and Aurel Wintner, On the solutions of the equation of heat conduction, Amer. J. Math. 72 (1950), 367–395. MR 36412, DOI 10.2307/2372040
- Einar Hille, Les probabilités continues en chaîne, C. R. Acad. Sci. Paris 230 (1950), 34–35 (French). MR 32119
- Kiyoshi Itô and Henry P. McKean Jr., Diffusion processes and their sample paths, Die Grundlehren der mathematischen Wissenschaften, Band 125, Academic Press, Inc., Publishers, New York; Springer-Verlag, Berlin-New York, 1965. MR 0199891
- Tze Leung Lai, Space-time processes, parabolic functions and one-dimensional diffusions, Trans. Amer. Math. Soc. 175 (1973), 409–438. MR 334337, DOI 10.1090/S0002-9947-1973-0334337-X
- Petr Mandl, Analytical treatment of one-dimensional Markov processes, Die Grundlehren der mathematischen Wissenschaften, Band 151, Academia [Publishing House of the Czechoslovak Academy of Sciences], Prague; Springer-Verlag New York Inc., New York, 1968. MR 0247667
- Herbert Robbins and David Siegmund, Boundary crossing probabilities for the Wiener process and sample sums, Ann. Math. Statist. 41 (1970), 1410–1429. MR 277059, DOI 10.1214/aoms/1177696787
- H. Robbins and D. Siegmund, On the law of the iterated logarithm for maxima and minima, Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971) Univ. California Press, Berkeley, Calif., 1972, pp. 51–70. MR 0400364
- H. Robbins and D. Siegmund, Statistical tests of power one and the integral representation of solutions of certain partial differential equations, Bull. Inst. Math. Acad. Sinica 1 (1973), no. 1, 93–120. MR 321204 16. J. B. Serrin, A uniqueness theorem for a parabolic equation, Bull. Amer. Math. Soc. 60 (1954), 344 (Abstract).
- D. V. Widder, Positive temperatures on an infinite rod, Trans. Amer. Math. Soc. 55 (1944), 85–95. MR 9795, DOI 10.1090/S0002-9947-1944-0009795-2
- D. V. Widder, Positive temperatures on a semi-infinite rod, Trans. Amer. Math. Soc. 75 (1953), 510–525. MR 58104, DOI 10.1090/S0002-9947-1953-0058104-7
Additional Information
- Journal: Bull. Amer. Math. Soc. 79 (1973), 1210-1215
- MSC (1970): Primary 60J50, 35K15, 35K20, 60J60; Secondary 60G45
- DOI: https://doi.org/10.1090/S0002-9904-1973-13382-8
- MathSciNet review: 0343382