Mean properties for the solutions of elliptic systems.

Jacqueline Détraz

Publicacions Matemàtiques (1993)

  • Volume: 37, Issue: 1, page 83-89
  • ISSN: 0214-1493


In this article, we consider the set F of functions annihilated by a uniformly elliptic system S in an open set Ω of Rn.We show that, as in the case of harmonic functions, F satisfies a submean-property, first for p=2 by elliptic estimates, then for all p > 0:|∇k u(x)|p ≤ C / (rn+kp) ∫B(x,r) |u(y)|p dyfor each u in F, each k > 0 and every ball B(x,r) included in Ω.As a consequence, we can compare ||u||Lp(Ω) and ||∇ku||Lp(Ω,δkp) where δ is the distance to the boundary of Ω, under the hypothesis that S has constant coefficients or satisfies S(1) = 0.We conclude that, with the metric ||u||Lp(Ω) + ||∇u||Lp(Ω) we have a compacity property of the ball of F for all p > 0.

How to cite


Détraz, Jacqueline. "Propriétés de moyenne pour les solutions de systèmes elliptiques." Publicacions Matemàtiques 37.1 (1993): 83-89. <>.

author = {Détraz, Jacqueline},
journal = {Publicacions Matemàtiques},
keywords = {Ecuaciones diferenciales elípticas; Función armónica; submean-property},
language = {fre},
number = {1},
pages = {83-89},
title = {Propriétés de moyenne pour les solutions de systèmes elliptiques},
url = {},
volume = {37},
year = {1993},

AU - Détraz, Jacqueline
TI - Propriétés de moyenne pour les solutions de systèmes elliptiques
JO - Publicacions Matemàtiques
PY - 1993
VL - 37
IS - 1
SP - 83
EP - 89
LA - fre
KW - Ecuaciones diferenciales elípticas; Función armónica; submean-property
UR -
ER -

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