The existence of regular boundary points for non-linear elliptic systems

By Frank Duzaar, Jan Kristensen, Giuseppe Mingione. 2007

64 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/c91c0faab785c61bb9b8f57a0e35a7f3e3b6ae30

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Regularity of minima: An invitation to the dark side of the calculus of variations (2006, background): “The first results in this direction can be found in my papers [248] [249], that I will summarize now, also keeping into account of some later improvements in [206] [98].”
Local Lipschitz regularity for degenerate elliptic systems (2009, result): “LOCAL LIPSCHITZ REGULARITY FOR DEGENERATE ELLIPTIC SYSTEMS 9 In the way stated above the result can be deduced from the stronger results available in the literature, see for instance in [2, 9, 27, 23].”
The boundary regularity of non-linear parabolic systems I (2010, methodology): “16) in [15] we infer the following properties of the vector field ah: ⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨ ⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩ ∣∣ah(z,w)∣∣+ (1 + |w|)∣∣∂wah(z,w)∣∣ L(1 + |w|), 〈 ∂wah(z,w)w̃, w̃ 〉 ν|w̃|2, ν|w − w̃|2 〈ah(z, w̃) − ah(z,w), w̃ − w〉, ν 2 |w|2 − L2/ν 〈ah(z,w),w〉, ∣∣ah(z,w) − a(z,w)∣∣ Lθ̃(|h|)(1 + |w|), ∣∣ah(x, t,”
Parabolic systems with polynomial growth and regularity (2011, methodology): “11) on β is something which is already present in dimension estimates for the elliptic case [30, 61, 62, 63], and says that higher regularity with respect to the coefficients allows us to get better estimates of the singular sets.”
Boundary Regularity in Variational Problems (2010, background): “In fact full boundary regularity follows in such cases, a result that is known to fail in the general vectorial case (see [23]).”