[Techniques λ-bonnes généralisées et applications à la régularité de Lorentz pondérée des équations elliptiques quasi linéaires]
Le but de cette Note est de donner des conditions suffisantes, dites λ-bonnes généralisées, pour la comparaison de deux fonctions mesurables dans les espaces de Lorentz pondérés. De plus, nous présentons des applications de ces résultats aux estimations de gradient des solutions aux problèmes elliptiques quasi linéaires dans les espaces de Lorentz pondérés.
The aim of this paper is to give some sufficient conditions, called generalized good-λ conditions, to obtain the weighted Lorentz comparisons between two measurable functions. Moreover, we also present several applications of these results for the gradient estimates of solutions to quasilinear elliptic problems in weighted Lorentz spaces.
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@article{CRMATH_2019__357_8_664_0,
author = {Tran, Minh-Phuong and Nguyen, Thanh-Nhan},
title = {Generalized good-\protect\emph{\ensuremath{\lambda}} techniques and applications to weighted {Lorentz} regularity for quasilinear elliptic equations},
journal = {Comptes Rendus. Math\'ematique},
pages = {664--670},
publisher = {Elsevier},
volume = {357},
number = {8},
year = {2019},
doi = {10.1016/j.crma.2019.08.002},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2019.08.002/}
}
TY - JOUR AU - Tran, Minh-Phuong AU - Nguyen, Thanh-Nhan TI - Generalized good-λ techniques and applications to weighted Lorentz regularity for quasilinear elliptic equations JO - Comptes Rendus. Mathématique PY - 2019 SP - 664 EP - 670 VL - 357 IS - 8 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2019.08.002/ DO - 10.1016/j.crma.2019.08.002 LA - en ID - CRMATH_2019__357_8_664_0 ER -
%0 Journal Article %A Tran, Minh-Phuong %A Nguyen, Thanh-Nhan %T Generalized good-λ techniques and applications to weighted Lorentz regularity for quasilinear elliptic equations %J Comptes Rendus. Mathématique %D 2019 %P 664-670 %V 357 %N 8 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2019.08.002/ %R 10.1016/j.crma.2019.08.002 %G en %F CRMATH_2019__357_8_664_0
Tran, Minh-Phuong; Nguyen, Thanh-Nhan. Generalized good-λ techniques and applications to weighted Lorentz regularity for quasilinear elliptic equations. Comptes Rendus. Mathématique, Tome 357 (2019) no. 8, pp. 664-670. doi : 10.1016/j.crma.2019.08.002. http://www.numdam.org/articles/10.1016/j.crma.2019.08.002/
[1] Global Lorentz and Lorentz-Morrey estimates below the natural exponent for quasilinear equations, Calc. Var. Partial Differ. Equ., Volume 54 (2015) no. 3, pp. 3107-3139
[2] Global weighted estimates for the gradient of solutions to nonlinear elliptic equations, Ann. Inst. Henri Poincaré, Anal. Non Linéaire, Volume 30 (2013), pp. 291-313
[3] Elliptic equations with BMO coefficients in Reifenberg domains, Commun. Pure Appl. Math., Volume 57 (2004), pp. 1283-1310
[4] Elliptic equations with BMO nonlinearity in Reifenberg domains, Adv. Math., Volume 219 (2008) no. 6, pp. 1937-1971
[5] Nonlinear elliptic equations with BMO coefficients in Reifenberg domains, J. Funct. Anal., Volume 250 (2007) no. 1, pp. 167-196
[6] On estimates for elliptic equations in divergence form, Commun. Pure Appl. Math., Volume 51 (1998) no. 1, pp. 1-21
[7] Calderón–Zygmund estimates ans non-uniformly elliptic operators, J. Funct. Anal., Volume 136 (2016) no. 4, pp. 1416-1478
[8] Gradient estimates via linear and nonlinear potentials, J. Funct. Anal., Volume 259 (2010), pp. 2961-2998
[9] Gradient estimates via non-linear potentials, Amer. J. Math., Volume 133 (2011), pp. 1093-1149
[10] Classical and Modern Fourier Analysis, Pearson/Prentice Hall, 2004
[11] Dynamic scaling of growing interfaces, Phys. Rev. Lett., Volume 56 (1986), pp. 889-892
[12] The Hardy-Littlewood maximal function of a Sobolev function, Isr. J. Math., Volume 100 (1997), pp. 117-124
[13] Regularity of the fractional maximal function, Bull. Lond. Math. Soc., Volume 35 (2003), pp. 529-535
[14] Universality classes for deterministic surface growth, Phys. Rev. A (3), Volume 38 (1988), pp. 4271-4283
[15] Linear potentials in nonlinear potential theory, Arch. Ration. Mech. Anal., Volume 207 (2013) no. 1, pp. 215-246
[16] Weighted and regularity estimates for nonlinear equations on Reifenberg flat domains, J. Differ. Equ., Volume 250 (2011) no. 5, pp. 2485-2507
[17] Global estimates for quasilinear elliptic equations on Reifenberg flat domains, Arch. Ration. Mech. Anal., Volume 203 (2012) no. 1, pp. 189-216
[18] The Calderón-Zygmund theory for elliptic problems with measure data, Ann. Sc. Norm. Super. Pisa, Cl. Sci. (V), Volume 6 (2007), pp. 195-261
[19] Potential estimates and quasilinear parabolic equations with measure data | arXiv
[20] Good-λ and Muckenhoupt–Wheeden type bounds, with applications to quasilinear elliptic equations with gradient power source terms and measure data, Math. Ann., Volume 374 (2019), pp. 67-98
[21] Nonlinear Muckenhoupt-Wheeden type bounds on Reifenberg flat domains, with applications to quasilinear Riccati type equations, Adv. Math., Volume 250 (2014), pp. 387-419
[22] Good-λ type bounds of quasilinear elliptic equations for the singular case, Nonlinear Anal., Volume 178 (2019), pp. 266-281
[23] Existence of a renormalized solution to the quasilinear Riccati-type equation in Lorentz spaces, C. R. Acad. Sci. Paris, Ser. I, Volume 357 (2019), pp. 59-65
[24] Lorentz-Morrey global bounds for singular quasilinear elliptic equations with measure data, Commun. Contemp. Math. (2019) | DOI
[25] New gradient estimates for solutions to quasilinear divergence form elliptic equations with general Dirichlet boundary data, J. Differ. Equ. (2019) | DOI
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