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ESAIM: Control, Optimisation and Calculus of Variations (1)

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On the continuity of degenerate n-harmonicfunctions
Flavia Giannetti, Antonia Passarelli di Napoli
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 18 / Issue 3 / July 2012

Published online by Cambridge University Press:

14 September 2011, pp. 621-642

Print publication:

July 2012
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We study the regularity of finite energy solutions to degeneraten-harmonic equations. The functionK(x), which measures the degeneracy, is assumed to besubexponentially integrable, i.e. it verifies the condition exp(P(K)) ∈ Lloc1. The function P(t) is increasing on [0,∞[ and satisfies the divergence condition \begin{equation}\int_1^\infty\frac{P(t)}{t^2}\,{\rm d}t=\infty.\end{equation} $\int_{1}^{\infty} \frac{P (t)}{t^{2}} d t = \infty .$