Gradient estimates below the duality exponent

By Giuseppe Mingione. 2010

279 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/cf8d1ec1e8c609e52cb41009dfbe11dd0602b65c

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Global Estimates for Quasilinear Elliptic Equations on Reifenberg Flat Domains (2012, background): “where the right-hand side is an integrable function, f ∈ L γ ; θ (�) .I n [ 31, Theorem 1 ], it is shown that for A(x) just measurable and 1 31 ], the range of γ is optimal for this class of coefficients.”
Linear Potentials in Nonlinear Potential Theory (2013, background): “1) is considered, the results in [1,2,6,9,16,31] can be now recovered.”
Potential estimates and gradient boundedness for nonlinear parabolic systems (2012, background): “We refer to [32], [33] and [34] for a more detailed description of the setting and for further references.”
Regularity for quasilinear equations on degenerate singular sets (2012, background): “1) has become accessible just quite recently, through a rather sophisticated and powerful nonlinear potential theory, see [4, 7, 13, 14, 15].”
Lorentz estimates for degenerate and singular evolutionary systems (2013, methodology): “…techniques we employ here were born as parabolic ones, see the forthcoming Section 2; hence we opt to present in a more detailed way the proof in the time-dependent setting, in order to show the basic points of the argument, and then show how to modify such proof to get the (simpler) elliptic one.”
Second-Order Two-Sided Estimates in Nonlinear Elliptic Problems (2017, background): “Fractional-order regularity for the gradient of solutions to nonlinear equations of p-Laplacian type is the subject of [4,16,54].”
Gradient estimates via non-linear potentials (2009, background): “tively. The estimates in (6.13) refer to Rn+1 as supporting domain, but they can be localized using cut-oﬀ functions and therefore yield local estimates for caloric Riesz potentials; see for instance [48, 49]. The ﬁnal outcome is the following result: Theorem 6.1. Let u ∈ L 1(−T,0;W1, (Ω)) be a SOLA”
Weighted and regularity estimates for nonlinear equations on Reifenberg flat domains (2011, background): “4 gives a global result over rough domains with an explicit quantification of the degree of integrability, Theorem 4 of [21] (when p = 2) gives a local result under a weak assumption on the nonlinearity, namely a(ξ, x) is just a measurable function in x.”
Parabolic systems with polynomial growth and regularity (2011, unknown): “For such aspects we refer to [35, 36, 66, 67, 50].”
Gradient potential estimates (2011, background): “19) also implies estimates in noninterpolation spaces such as Morrey spaces, of the type obtained in [27, 28, 29]; see also the forthcoming papers [16, 17].”
Nonlinear Measure Data Problems (2011, methodology): “Combining some of the ingredients of the above proof with the methods from [78] it is possible to give another proof of Theorem 4.”