Bibliography
Friedman, A.: Partial differential equations of parabolic type. Englewood Cliffs, N.J.: Prentice-Hall 1964.
—— Remarks on the maximum principle for parabolic equations. Pacific J. Math.8, 201–211 (1958).
Il'in, A. N., A. S. Kalashnikov, and O. A. Oleinik: Second order linear equations of parabolic type. Uspekhi Mat. Nauk. S.S.S.R.17, 3–146 (1962). Translated in Russian Math. Surveys17, no. 3, 1–143 (1962).
Karlin, S.: Total positivity, absorption probabilities, and applications. Transactions Amer. Math. Soc.111, 33–107 (1964).
Oleinik, O. A.: Construction of a generalized solution of the Cauchy problem for a quasilinear equation of first order by the introduction of “Vanishing Viscosity.” Uspekhi Mat. Nauk. S.S.S.R.14, no. 2, 159–164 (1959). Translated as Amer. Math. Soc. Trans., vol.33, ser. 2.
Vyborny, R.: The properties of solutions of certain boundary value problems for parabolic equations. Dokl. Akad. Nauk.117, 4, 563–565 (1957) (Russian).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sattinger, D.H. On the total variation of solutions of parabolic equations. Math. Ann. 183, 78–92 (1969). https://doi.org/10.1007/BF01361263
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01361263