Tohoku Mathematical Journal

Stokes' theorem, volume growth and parabolicity

Daniele Valtorta and Giona Veronelli

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We present some new Stokes' type theorems on complete non-compact manifolds that extend, in different directions, previous works by Gaffney and Karp and also the so called Kelvin-Nevanlinna-Royden criterion for $p$-parabolicity. Applications to comparison and uniqueness results involving the $p$-Laplacian are deduced.

Article information

Tohoku Math. J. (2) Volume 63, Number 3 (2011), 397-412.

First available: 11 October 2011

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Mathematical Reviews number (MathSciNet)

Primary: 35B05: Oscillation, zeros of solutions, mean value theorems, etc.
Secondary: 31C45: Other generalizations (nonlinear potential theory, etc.)

$p$-parabolicity Stokes' theorem Kelvin-Nevanlinna-Royden criterion


Valtorta, Daniele; Veronelli, Giona. Stokes' theorem, volume growth and parabolicity. Tohoku Mathematical Journal 63 (2011), no. 3, 397--412. doi:10.2748/tmj/1318338948.

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