Nonlinear elliptic equations with BMO coefficients in Reifenberg domains

By Sun-Sig Byun, Lihe Wang, Shulin Zhou. 2007

351 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/a2672be0442887ee9c43c50af7fc4b29335d0754

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In Applied Mathematics

1. Sun-Sig Byun
2. Giuseppe Mingione
3. N. Phuc
4. Jihoon Ok
5. Lihe Wang
6. Hongjie Dong
7. Doyoon Kim
8. Tadele Mengesha

In Computational Theory and Mathematics

1. Sun-Sig Byun
2. N. Phuc
3. Giuseppe Mingione
4. Lihe Wang
5. Jihoon Ok
6. Hongjie Dong
7. Doyoon Kim
8. Tadele Mengesha

Citations in the corpus

• Gradient estimates for elliptic equations with Lp(·)logL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^{p(\cdot )}\ (2016, methodology): “The method used in this paper is influenced by the ones in [2,5,7] which are based on [9].”
• Global Estimates for Quasilinear Elliptic Equations on Reifenberg Flat Domains (2012, methodology): “In addition, this small BMO condition has been used in various works as an appropriate substitute for the Sarason VMO (vanishing mean oscillation [38]) condition (see, for example, [4, 5 ,16,20,30,39,41]).”
• Nonlinear gradient estimates for elliptic equations of general type (2012, methodology): “The result in [7] is extended to the setting of Orlicz space by Byun et al.”
• Lorentz estimates for degenerate and singular evolutionary systems (2013, neutral): “For the case q = ∞, the space L(γ,∞)(A), 1 ≤ γ ∞, is nothing else than the Marcinkiewicz space Mγ(A), that is the space of measurable functions g such that ‖g‖L(γ,∞)(A) = ‖g‖Mγ(A) := sup λ>0 ( λγ ∣∣{ξ ∈ A : |g(ξ)| > λ}∣∣) 1γ <∞.”
• Gradient estimates for elliptic systems in non-smooth domains (2008, methodology): “We should point out that the techniques used in [4–6,8] rely on maximal function approach.”
• Elliptic Equations in Divergence Form with Partially BMO Coefficients (2008, methodology): “For equations in a so-called Reifenberg flat domain, the solvability of the Dirichlet problem and the conormal derivative problem was established in [5] and [6].”
• Morrey global bounds and quasilinear Riccati type equations below the natural exponent (2014, methodology): “A proof of this lemma, which uses Lebesgue Differentiation Theorem and the standard Vitali covering lemma, can be found in [15] with obvious modifications to fit the setting here.”
• On $L_p$-estimates for elliptic and parabolic equations with $A_p$ weights (2016, background): “For equations/systems in Reifenberg flat domain and the level set type argument, see, for instance, [7, 18].”
• Parabolic equations in time dependent Reifenberg domains (2007, methodology): “The main purpose in this work is to develop tools of analysis for a complete parabolic analogue of the result in [5].”
• Parabolic Equations in Reifenberg Domains (2005, result): “This work is a natural follow up to the results in [ 7 ] where Byun &W ang have discussed suitable and minimal conditions on the coefficients and domains for the W 1,p theory, 1 <p< ∞, for the divergence form elliptic equations.”
• Calderón–Zygmund theory for nonlinear elliptic problems with irregular obstacles (2012, methodology): “Thanks to this measure density condition, the Reifenberg domains are W 1,t -extension domains, 1 t ∞ and the usual extension theorem, Sobolev’s inequality and Poincaré’s inequality hold true on the Reifenberg domains, see [5,21,23,24,27] and the references therein.”
• Pointwise Calderón–Zygmund gradient estimates for the p -Laplace system (2015, background): “Recent global gradient estimates for boundary value problems, under minimal regularity assumptions on the boundary of the ground domain, are the object of [2, 5, 10, 16, 17, 53, 43, 44].”
• Boundary Estimates in Elliptic Homogenization (2015, background): “We remark that theW 1,p estimates (local or global) for operators with nonsmooth coefficients in nonsmooth domains are of interest in their own rights and have been studied extensively in recent years (see [11, 45, 8, 39, 9, 34, 10, 41, 13, 29, 16, 18] and their references).”
• On the extension property of Reifenberg-flat domains (2012, methodology): “[4] S. Byun, L. Wang, and S. Zhou.”
• Higher order elliptic and parabolic systems with variably partially BMO coefficients in regular and irregular domains (2011, neutral): “KIM developed by the same authors in [4], which in turn uses an idea of approximations originally due to Caffarelli; see [8].”
• Elliptic equations with measurable coefficients in Reifenberg domains (2010, methodology): “For a precise definition of (δ,R)-Reifenberg flatness condition see [3–5].”