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Unique Continuation Property of Non-Positive Weak Subsolutions for Parabolic Equations of Higher Order

Published online by Cambridge University Press:  22 January 2016

Kazunari Hayashida
Kazunari Hayashida*
Affiliation:
Research Institute for Mathematical Sciences, Kyoto University
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When L is a parabolic differential operator of second order, Nirenberg [6] proved the maximum principle for the function u which has second order continuous derivatives and satisfies Lu≧0. Recently Friedman [2] has proved the maximum principle for the measurable function satisfying Lu≧O in the wide sense. This function is named a weakly L-subparabolic function. On the other hand, Littman [5] earlier than Friedman, has defined a weakly A- subharmonic function for an elliptic differential operator A of second order and has showed the maximum principle for it.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 24 , June 1964 , pp. 241 - 248
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1964

References

[1] Friedman, A., Uniqueness properties in the theory of differential operators of elliptic type, Jour. Math. Mech., 7 (1958), 61–67.Google Scholar
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[3] Hayashida, K., Unique continuation theorem of elliptic systems of partial differential equations, Proc. Japan Acad., 38 (1962), 630–635.Google Scholar
[4] Hayashida, K., A note on a weak subsolution, Proc. Japan Acad., 39 (1963), 203–207.Google Scholar
[5] Littman, W., A strong maximum principle for weakly L-subharmonic functions, Jour. Math. Mech., 8 (1959), 761–770.Google Scholar
[6] Nirenberg, L., A strong maximum principle for parabolic equations, Comm. Pure Appl. Math., 6 (1953), 167–177.CrossRefGoogle Scholar
[7] Pederson, R. N., On the order of zeros of one-signed solutions of elliptic equations, Jour. Math. Mech., 8 (1959), 193–196.Google Scholar