Soit un système elliptique d’ordre d’opérateurs différentiels homogènes. On établit l’équivalence entre la norme de la fonction maximale et la fonctionnelle quadratique des solutions de dans les domaines lipschitziens. On donne quelques conséquences de ce résultat.
Let be an elliptic system of higher order homogeneous partial differential operators. We establish in this article the equivalence in norm between the maximal function and the square function of solutions to in Lipschitz domains. Several applications of this result are discussed.
@article{AIF_1997__47_5_1425_0, author = {Dahlberg, Bj\"orn E. J. and Kenig, Carlos E. and Pipher, Jill and Verchota, G. C.}, title = {Area integral estimates for higher order elliptic equations and systems}, journal = {Annales de l'Institut Fourier}, volume = {47}, year = {1997}, pages = {1425-1461}, doi = {10.5802/aif.1605}, mrnumber = {98m:35045}, zbl = {0892.35053}, language = {en}, url = {http://dml.mathdoc.fr/item/AIF_1997__47_5_1425_0} }
Dahlberg, Björn E. J.; Kenig, Carlos E.; Pipher, Jill; Verchota, G. C. Area integral estimates for higher order elliptic equations and systems. Annales de l'Institut Fourier, Tome 47 (1997) pp. 1425-1461. doi : 10.5802/aif.1605. http://gdmltest.u-ga.fr/item/AIF_1997__47_5_1425_0/
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