# On the continuity of degenerate n-harmonic functions

• Volume: 18, Issue: 3, page 621-642
• ISSN: 1292-8119

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## Abstract

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We study the regularity of finite energy solutions to degenerate n-harmonic equations. The function K(x), which measures the degeneracy, is assumed to be subexponentially integrable, i.e. it verifies the condition exp(P(K)) ∈ Lloc1. The function P(t) is increasing on  [0,∞[  and satisfies the divergence condition ${\mathrm{\int }}_{\mathrm{1}}^{\mathrm{\infty }}\frac{\mathit{P}\mathrm{\left(}\mathit{t}\mathrm{\right)}}{{\mathit{t}}^{\mathrm{2}}} \mathrm{d}\mathit{t}\mathrm{=}\mathrm{\infty }\mathit{.}$

## How to cite

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Giannetti, Flavia, and Passarelli di Napoli, Antonia. "On the continuity of degenerate n-harmonic functions." ESAIM: Control, Optimisation and Calculus of Variations 18.3 (2012): 621-642. <http://eudml.org/doc/244353>.

@article{Giannetti2012,
abstract = {We study the regularity of finite energy solutions to degenerate n-harmonic equations. The function K(x), which measures the degeneracy, is assumed to be subexponentially 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\}},
author = {Giannetti, Flavia, Passarelli di Napoli, Antonia},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Orlicz classes; degenerate elliptic equations; continuity; n-harmonic functions; regularity of solution; finite energy solutions},
language = {eng},
month = {11},
number = {3},
pages = {621-642},
publisher = {EDP Sciences},
title = {On the continuity of degenerate n-harmonic functions},
url = {http://eudml.org/doc/244353},
volume = {18},
year = {2012},
}

TY - JOUR
AU - Giannetti, Flavia
AU - Passarelli di Napoli, Antonia
TI - On the continuity of degenerate n-harmonic functions
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2012/11//
PB - EDP Sciences
VL - 18
IS - 3
SP - 621
EP - 642
AB - We study the regularity of finite energy solutions to degenerate n-harmonic equations. The function K(x), which measures the degeneracy, is assumed to be subexponentially integrable, i.e. it verifies the condition exp(P(K)) ∈ Lloc1. The function P(t) is increasing on  [0,∞[  and satisfies the divergence condition $$\int_1^\infty\frac{P(t)}{t^2}\,{\rm d}t=\infty.$$
LA - eng
KW - Orlicz classes; degenerate elliptic equations; continuity; n-harmonic functions; regularity of solution; finite energy solutions
UR - http://eudml.org/doc/244353
ER -

## References

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