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

DOI:
https://doi.org/10.1090/S0002-9947-1983-0709568-3

MathSciNet review:
709568

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Abstract | References | Similar Articles | Additional Information

Abstract: Integral averages of weak subsolutions (and supersolutions) in 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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Additional Information

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