In this paper we prove existence of solutions to some elliptic systems with measure on the right hand side, in dimension two and three.
@article{BUMI_2011_9_4_1_137_0,
author = {Francesco Leonetti and Pier Vincenzo Petricca},
title = {Nonlinear Elliptic Systems with Measure Data in Low Dimension},
journal = {Bollettino dell'Unione Matematica Italiana},
volume = {4},
year = {2011},
pages = {137-146},
zbl = {1236.35194},
mrnumber = {2797470},
language = {en},
url = {http://dml.mathdoc.fr/item/BUMI_2011_9_4_1_137_0}
}
Leonetti, Francesco; Petricca, Pier Vincenzo. Nonlinear Elliptic Systems with Measure Data in Low Dimension. Bollettino dell'Unione Matematica Italiana, Tome 4 (2011) pp. 137-146. http://gdmltest.u-ga.fr/item/BUMI_2011_9_4_1_137_0/
[1] - - - - - , An theory of exixtence and uniqueness of solutions of nonlinear elliptic equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 22 (1995), 241-273. | MR 1354907
[2] , Problemi differenziali ellittici e parabolici con dati misure, Boll. Un. Mat. Ital. A, 11 (1997), 439-461.
[3] - , Non-linear Elliptic and Parabolic Equations involving Measure Data, J. Funct. Anal., 87 (1989), 149-169. | MR 1025884 | Zbl 0707.35060
[4] - - , Anisotropic equations in , Differential and Integral Equations, 9 (1996), 209-212. | MR 1364043 | Zbl 0838.35048
[5] , Approximated solutions of equations with data. Application to the H-convergence of quasi-linear parabolic equations, Ann. Mat. Pura Appl., 185 (1996), 207-240. | MR 1441620
[6] - - - , Renormalized solutions of elliptic equations with general measure data, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 28 (1999), 741-808. | MR 1760541 | Zbl 0958.35045
[7] - - , The p-harmonic systems with measure-valued right hand side, Ann. Inst. H. Poincare Anal. Non Lineaire, 14 (1997), 353-364. | MR 1450953 | Zbl 0879.35052
[8] - - , Non-linear elliptic systems with measure-valued right hand side, Math. Z., 226 (1997), 545-574. | MR 1484710 | Zbl 0895.35029
[9] - , Non-linear elliptic systems involving measure data, Rendiconti di Matematica, serie VII Volume 15, Roma (1995), 311-319. | MR 1339247 | Zbl 0838.35133
[10] - - , Inverting the p-harmonic operator, Manuscripta Math., 92 (1997), 249-258. | MR 1428651 | Zbl 0869.35037
[11] , Maximum principle for vector-valued minimizers of some integral functionals, Boll. Un. Mat. Ital., 5-A (1991), 51-56. | MR 1101010 | Zbl 0729.49015
[12] - , Existence of bounded solutions to some nonlinear degenerate elliptic systems, Discrete Cont. Dyn. Syst. Ser. B, 11 (2009), 191-203. | MR 2461817 | Zbl 1159.35337
[13] - , Regularity for solutions to some nonlinear elliptic systems, Complex Var. Elliptic Equ., (2010), DOI: 10.1080/17476933.2010.487208. | MR 2852081 | Zbl 1224.35139
[14] - , Quelques resultats de Visik sur les problemes elliptiques non lineaires par les methodes de Minty-Browder, Bull. Soc. Math. Fr., 93 (1965), 97-107. | MR 194733 | Zbl 0132.10502
[15] , The Calderon-Zygmund theory for elliptic problems with measure data, Ann. Sc. Norm. Sup. Pisa, 6 (2007), 195-261. | MR 2352517 | Zbl 1178.35168
[16] , Gradient estimates below the duality exponent, Math. Ann., 346 (2010), 571-627. | MR 2578563 | Zbl 1193.35077
[17] , Pathological solutions of elliptic differential equations, Ann. Scuola Norm. Sup. Pisa, 18 (1964), 385-387. | MR 170094 | Zbl 0142.37601
[18] , A note on nonlinear elliptic systems involving measures, Electronic Journal of Differential Equations, Vol 2000, No. 08 (2000), 1-6. | MR 1735065 | Zbl 0939.35063