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On the positivity of weak supersolutions of non-uniformly elliptic equations

Published online by Cambridge University Press:  17 April 2009

Neil S. Trudinger
Neil S. Trudinger
Affiliation:
Department of Pure Mathematics, School of General Studies, Australian National University, Canberra, ACT.
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Abstract

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The classical maximum principle for homogeneous, second order, uniformly elliptic equations implies that non-negative, classical supersolutions are either positive or vanish identically in the interior of their domain of definition. This paper is concerned with an extension of this result to weak supersolutions of non-uniformly elliptic equations subject to only mild coefficient restrictions.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 19 , Issue 3 , December 1978 , pp. 321 - 324
Copyright
Copyright © Australian Mathematical Society 1979

References

[1]Coffman, C.V., Duffin, R. and Mizel, V.J., “Positivity of weak solutions of non-uniformly elliptic equations”, Ann. Mat. Pura Appl. (4) 104 (1975), 209–238.CrossRefGoogle Scholar
[2]Morrey, Charles B. Jr, Multiple integrals in the calculus of variations (Die Grundlehren der mathematischen Wissenschaften, 130. Springer-Verlag, Berlin, Heidelberg, New York, 1966).Google Scholar
[3]Trudinger, Neil S., “Linear elliptic operators with measurable coefficients”, Ann. Scuola. Norm. Sup. Pisa (3) 27 (1973), 265–308.Google Scholar
[4]Trudinger, Neil S., “Maximum principles for linear, non-uniformly elliptic operators with measurable coefficients”, Math. Z. 156 (1977), 291–301.CrossRefGoogle Scholar