The Singular Set of Solutions to Non-Differentiable Elliptic Systems

By Giuseppe Mingione. 2003

149 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/96e113ae5fc0827b5efb5b6c1ac181e2a0936114

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Global Boundedness of the Gradient for a Class of Nonlinear Elliptic Systems (2012, result): “Recent improvements of these results in terms of Hausdorff measures can be found in [35,50,51].”
Fractional Differentiability for Solutions of Nonlinear Elliptic Equations (2016, methodology): “We’d like to mention that in [21] a Besov-Nikoski estimate for the gradient of the solutions with an higher integrability exponent p > 2 is obtained through the application of the Gehring Lemma to the difference quotients.”
Second order parabolic systems, optimal regularity, and singular sets of solutions (2005, methodology): “The following lemma is a (parabolic variant) of a well known measure theoretical result; the proof c obtained along the lines of [19], Chapter 3 and [30], Section 4.”
The Singular Set of Minima of Integral Functionals (2006, result): “As the functional is convex there is no difference between its minimizers and its critical points, that is, the minimizers are precisely the weak solutions of the Euler-Lagrange system, divfz(x, Du) = 0. It can be shown that conditions (1.1) also imply that the vector field x � fz(x, z)/(|z |+ 1) is”
Bounds for the singular set of solutions to non linear elliptic systems (2003, methodology): “We shall sketch the main ideas, referring to [ 25 ] for further details.”
The boundary regularity of non-linear parabolic systems I (2010, result): “We remark that a similar strategy was developed for the elliptic case to get first singular sets estimates in the interior [28,29], and then at the boundary [15], and [16,18] for the interior parabolic case; we refer to [25–27] for results concerning the stationary variational case.”
Fractional estimates for non-differentiable elliptic systems with general growth (2008, background): “In his two articles [19] and [20] Mingione gave the answer to this question in the case pb 2, i.”
The existence of regular boundary points for non-linear elliptic systems (2007, methodology): “The proof of the above theorems is based on an up-to-the-boundary fractional di¤erentiability estimate for the gradient Du, that extends the interior results of [37].”
The Singular Set of ω-minima (2005, background): “We conclude this section by recalling a general property of fractional Sobolev functions (for an elementary proof refer to [15], Section 4).”
The Calderón-Zygmund theory for elliptic problems with measure data (2006, background): “The following result is classical in potential theory [3]; see again [59] for an elementary proof that avoids potential theory.”
The Singular Set of Lipschitzian Minima of Multiple Integrals (2007, result): “Similar results hold for weak solutions to elliptic systems [28,29]; for an account of results on partial regularity and singular sets of minima we refer to [30].”
An Introduction to the Regularity Theory for Elliptic Systems, Harmonic Maps and Minimal Graphs (2005, methodology): “In the case of solutions to nonlinear elliptic systems similar estimates were obtained by Mingione in [73, 74].”