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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Mean values of subsolutions of elliptic and parabolic equations


Author: William P. Ziemer
Journal: Trans. Amer. Math. Soc. 279 (1983), 555-568
MSC: Primary 35D99; Secondary 35B99, 35J60, 35K55
MathSciNet review: 709568
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Abstract: Integral averages of weak subsolutions (and supersolutions) in $ {R^n}$ of quasilinear elliptic and parabolic equations are investigated. The important feature is that these integral averages are defined in terms of measures that reflect interesting geometric phenomena. Harnack type inequalities are established in terms of these integral averages.


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DOI: https://doi.org/10.1090/S0002-9947-1983-0709568-3
Keywords: Lebesgue points, Harnack inequahties, Moser iteration
Article copyright: © Copyright 1983 American Mathematical Society