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.
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.
@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}, pages = {1425--1461}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {47}, number = {5}, year = {1997}, doi = {10.5802/aif.1605}, zbl = {0892.35053}, mrnumber = {98m:35045}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1605/} }
TY - JOUR AU - Dahlberg, Björn E. J. AU - Kenig, Carlos E. AU - Pipher, Jill AU - Verchota, G. C. TI - Area integral estimates for higher order elliptic equations and systems JO - Annales de l'Institut Fourier PY - 1997 SP - 1425 EP - 1461 VL - 47 IS - 5 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1605/ DO - 10.5802/aif.1605 LA - en ID - AIF_1997__47_5_1425_0 ER -
%0 Journal Article %A Dahlberg, Björn E. J. %A Kenig, Carlos E. %A Pipher, Jill %A Verchota, G. C. %T Area integral estimates for higher order elliptic equations and systems %J Annales de l'Institut Fourier %D 1997 %P 1425-1461 %V 47 %N 5 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1605/ %R 10.5802/aif.1605 %G en %F 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, Volume 47 (1997) no. 5, pp. 1425-1461. doi : 10.5802/aif.1605. https://aif.centre-mersenne.org/articles/10.5802/aif.1605/
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