A boundary estimate for nonlinear equations with discontinuous coefficients

By Juha Kinnunen, Shulin Zhou. Differential and Integral Equations, 2001

79 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/538fda11bcd9e3a5edb63562bed7051abd2a3ba6

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In Applied Mathematics

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Citations in the corpus

Gradient estimates in Orlicz space for nonlinear elliptic equations (2008, unknown): “Their results were extended by Kinnunen and Zhou in [16,17] to the case A ∈ VMO and ∂Ω ∈ C1,α .”
Elliptic equations with BMO nonlinearity in Reifenberg domains (2008, methodology): “The goal of this paper is to formulate and prove a version of the results in [6,20,21] for such equations of nonvariational type.”
Elliptic equations with BMO coefficients in Lipschitz domains (2004, background): “We refer to [10, 11] for a general discussion on equation (1.”
On the connection between two quasilinear elliptic problems with source terms of order 0 or 1 (2008, background): “It improves the results of [11], [38], [4], [19] and extends the estimates of the gradient given in [46], [47] for solutions U 2 W 1;p 0 ( ).”
HIGHER INTEGRABILITY FOR WEAK SOLUTIONS OF HIGHER ORDER DEGENERATE PARABOLIC SYSTEMS (2008, result): “For similar results in the elliptic case see also the papers [15], [16] with the references therein.”
Global Calderón–Zygmund theory for nonlinear parabolic systems (2013, background): “These results were also achieved in a global version for homogeneous Dirichlet boundary data, i.e. u = 0 on the boundary by Kinnunen & Zhou [31] for C 1 ,α domains and by Byun & Wang [13] in Reifenberg domains.”
Gradient estimates for a class of parabolic systems (2007, methodology): “The extension to anisotropic elliptic equations with possibly discontinuous, vanishing mean oscillation (VMO) coefficients has been achieved by Kinnunen & Zhou [19, 20], while a class of general non-linear elliptic equations and systems in divergence form, under nonstandard growth conditions, has be”
Pointwise Calderón–Zygmund gradient estimates for the p -Laplace system (2015, background): “For instance, results on elliptic problems involving differential operators affected by weak regularity properties can be found in [24, 25, 7, 35, 36].”
Higher integrability for parabolic systems with non-standard growth and degenerate diffusions (2011, result): “For similar results concerning equations with VMO-coefficients we refer to [31], [32] and the references therein.”