We describe a few results obtained in [10], concerning the possibility of estimating solutions of quasilinear elliptic equations via nonlinear potentials.
@article{BUMI_2011_9_4_1_149_0,
author = {Tuomo Kuusi and Giuseppe Mingione},
title = {Endpoint and Intermediate Potential Estimates for Nonlinear Equations},
journal = {Bollettino dell'Unione Matematica Italiana},
volume = {4},
year = {2011},
pages = {149-157},
zbl = {1235.35132},
mrnumber = {2797471},
language = {en},
url = {http://dml.mathdoc.fr/item/BUMI_2011_9_4_1_149_0}
}
Kuusi, Tuomo; Mingione, Giuseppe. Endpoint and Intermediate Potential Estimates for Nonlinear Equations. Bollettino dell'Unione Matematica Italiana, Tome 4 (2011) pp. 149-157. http://gdmltest.u-ga.fr/item/BUMI_2011_9_4_1_149_0/
[1] - , Sobolev Spaces. Second edition, Pure and Appl. Math., 140, Elsevier/Academic Press, Amsterdam, 2003. | MR 2424078
[2] - , Nonlinear elliptic equations with right-hand side measures, Comm. PDE, 17 (1992), 641-655. | MR 1163440 | Zbl 0812.35043
[3] - , Maximal functions measuring smoothness, Mem. Amer. Math. Soc., 47, no. 293 (1984). | MR 727820 | Zbl 0529.42005
[4] - , Gradient estimates via nonlinear potentials, Amer. J. Math., to appear. | MR 2823872 | Zbl 1200.35313
[5] - , Gradient estimates via linear and nonlinear potentials, J. Funct. Anal., 259 (2010), 2961-2998. | MR 2719282 | Zbl 1200.35313
[6] - , Local Lipschitz regularity for degenerate elliptic systems, Ann. Inst. H. Poincaré Anal. Non Linèaire, 27 (2010), 1361-1396. | MR 2738325 | Zbl 1216.35063
[7] - , The Wiener test and potential estimates for quasilinear elliptic equations, Acta Math., 172 (1994), 137-161. | MR 1264000
[8] - , The singular set of minima of integral functionals, Arch. Ration. Mech. Anal., 180 (2006), 331-398. | MR 2214961 | Zbl 1116.49010
[9] - , Boundary regularity in variational problems, Arch. Rational Mech. Anal., 198 (2010), 369-455. | MR 2721587 | Zbl 1228.49043
[10] - , Universal potential estimates, Preprint 2010. | MR 2900466
[11] , Regularity of the gradient for a class of nonlinear possibly degenerate elliptic equations, Ph. D. Thesis, University of Washington, St. Louis.
[12] , Bounds for the singular set of solutions to non linear elliptic systems, Calc. Var. PDE, 18 (2003), 373-400. | MR 2020367 | Zbl 1045.35024
[13] , The Calderón-Zygmund theory for elliptic problems with measure data, Ann. Scu. Norm. Sup. Pisa Cl. Sci. (V), 6 (2007), 195-261. | MR 2352517 | Zbl 1178.35168
[14] , Gradient estimates below the duality exponent, Math. Ann., 346 (2010), 571-627. | MR 2578563 | Zbl 1193.35077
[15] , Gradient potential estimates, J. European Math. Soc., 13 (2011), 459-486. | MR 2746772 | Zbl 1217.35077
[16] , Nonlinear aspects of Calderón-Zygmund theory, Jahresbericht der DMV, 112 (2010), 159-191. | MR 2722503 | Zbl 1218.35104
[17] - , On the weak continuity of elliptic operators and applications to potential theory, Amer. J. Math., 124 (2002), 369-410. | MR 1890997 | Zbl 1067.35023
[18] - , Quasilinear elliptic equations with signed measure data, Disc. Cont. Dyn. Systems, 124 (2002), 369-410. | MR 2449089