Area integral estimates for higher order elliptic equations and systems

Dahlberg, Björn E. J.; Kenig, Carlos E.; Pipher, Jill; Verchota, G. C.

Annales de l'Institut Fourier, Tome 47 (1997) no. 5, pp. 1425-1461.

Soit $L$ un système elliptique d’ordre $m\ge 2$ d’opérateurs différentiels homogènes. On établit l’équivalence entre la norme $L^p$ de la fonction maximale et la fonctionnelle quadratique des solutions de $L$ dans les domaines lipschitziens. On donne quelques conséquences de ce résultat.

Let $L$ be an elliptic system of higher order homogeneous partial differential operators. We establish in this article the equivalence in $L^p$ norm between the maximal function and the square function of solutions to $L$ in Lipschitz domains. Several applications of this result are discussed.

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