On the weak continuity of elliptic operators and applications to potential theory

By Neil S. Trudinger, Xu-jia Wang. 2002

251 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/9fb34c36c92a13b7201ccc56140b985d91c9f533

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In Applied Mathematics

Citations in the corpus

Singular quasilinear and Hessian equations and inequalities (2009, methodology): “with the regular distributional gradient of u. In general we have the following gradient estimates [20] (see also [18], [ 34 ]).”
Removable sets for continuous solutions of quasilinear elliptic equations (2001, methodology): “Our method of proof combines some ideas from [K], [L], and [ TW ].”
Nonlinear Measure Data Problems (2011, methodology): “The main references here will be [53, 90, 37, 39, 68, 67, 79, 90, 91].”
Wiener regularity for large solutions of nonlinear equations (2003, background): “Trudinger and Wang presented in [73] an alternative, more general, and more concise approach to quasilinear equations of the second order.”
Convex functions on Carnot groups. (2007, methodology): “If u is not bounded below, we use the truncation uM(x) = max{−M, u(x)} and standard limit theorems (see [16].”
Gradient potential estimates (2011, background): “2 can also be considered as the higher order analog of that in [23, 31] when p = 2.”
Gradient estimates via non-linear potentials (2009, methodology): “42) are slightly stronger than those in [56].”
Gradient continuity estimates (2010, background): “the by now classical non-linear potential estimates for u in terms of Wolff potentials obtained in [25, 36 ,37].”
Harnack Inequalities: An Introduction (2007, background): “Degenerate elliptic operators: [67] establishes a Harnack inequality, [68] investigates Green’s functions; [69, 70] allow for different new kinds of weights; [71] studies X-elliptic operators; [72] further relaxes assumptions on the weights and allows for terms of lower order; [73] investigates quit”
Linear Potentials in Nonlinear Potential Theory (2013, background): “1 somehow unexpected is that, starting from the seminal papers of Kilpeläinen & Malý [18,19], with different approaches offered by Trudinger & Wang [38,39] (that also worked in the subelliptic setting, starting by the ideas in [37,36]) and Korte & Kuusi [20] and Duzaar & Mingione [9], it is a standa”
A priori estimates, positivity results, and nonexistence theorems for quasilinear degenerate elliptic inequalities (2010, background): “See also Trudinger and Wang [60] for related results.”
Regularity of minima: An invitation to the dark side of the calculus of variations (2006, background): “Even more importantly, as we shall see in a few lines, De Giorgi's insights opened the way to the nonlinear theory, and they are are the cornerstone of what is nowadays called " Non-linear Potential Theory " , see [181] [230] [227] [300].”
The Wolff gradient bound for degenerate parabolic equations (2014, methodology): “Another interesting approach to (1.6) was later given by Trudinger & Wang in [40, 41] and Kuusi & Korte in [22].”
Local Lipschitz regularity for degenerate elliptic systems (2009, background): “In this respect pointwise estimates for solutions are obtained in [22, 35, 30, 11].”
A nonlinear Stein theorem (2014, methodology): “Indeed, in contrast to [18], where the analysis was based on the use of potential estimates (see [14,24,25]), here we pursue a different path using directly certain characterisations of Lorentz spaces (see for instance Section 2.”