Boundary Regularity in Variational Problems

By Jan Kristensen, Giuseppe Mingione. 2010

133 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/9ac30b1fdec809275c856a669bdfc0e44374f934

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In Applied Mathematics

In Computational Mechanics

In Computational Theory and Mathematics

Citations in the corpus

On the Regularity of Minima of Non-autonomous Functionals (2019, result): “a weakly diﬀerentiable version. This approach has been introduced in the interesting papers [24,25], where Moser’s iteration has been employed; previous results involving Sobolev coeﬃcients appear in [42]. One our goals here is to describe a variant of Moser’s iteration, that, in a sense, allows to ”
Global Calderón–Zygmund theory for nonlinear parabolic systems (2013, background): “A ﬁrst result in this direction for the special case when F ∈ L ∞ has been obtained by Misawa [33]. time The local Calder´on & Zygmund theory for the dependent, parabolic case together with a quantitative estimate has been achieved by Acerbi & Mingione [3] and for more general non-linear systems by ”
Regularity for general functionals with double phase (2017, methodology): “5) |Vt(z1)− Vt(z2)| ≈ (|z1|+ |z2|) |z1 − z2| , that holds with involved constants depending only on n, t (see for instance [33, 34]).”
Parabolic systems with polynomial growth and regularity (2011, background): “The relation between the two aspects has been clarified, in the elliptic case, in the papers [52, 53, 62]; see also the surveys [63, 65].”
Higher differentiability of minimizers of variational integrals with Sobolev coefficients (2012, background): “Nevertheless, we would like to mention that in [24] the authors deal with functionals depend on the x-variable through a coefficient that belongs to a fractional Sobolev space but satisfies also a Hölder’s condition with arbitrarily small exponent.”
Higher differentiability for solutions to a class of obstacle problems (2018, background): “Kristensen, J., Mingione, G.: Boundary regularity in variational problems.”
Besov regularity for solutions of p-harmonic equations (2017, background): “Wemention previous contributions made in [2, 4, 5] for the case of planar Beltrami systems, and [16, 17] for higher dimensional results with not necessarily linear growth.”
Lipschitz Bounds and Nonautonomous Integrals (2020, methodology): “Then Du∈ L∞ loc(Ω;R N×n) and u∈ W2,2 loc (Ω;R N). Proof. The proof goes now in three diﬀerent steps, where we essentially revisit and readapt a few hidden facts in the literature. References [33] and [44] are particularly relevant here. Step 1: Regularized integrands. We revisit the procedure we use”
Fractional Differentiability for Solutions of Nonlinear Elliptic Equations (2016, unknown): “Such assumption, together with a Hölder continuity of the coefficients, has been already employed in [18], where various higher integrability results are obtained.”
Higher differentiability of minimizers of convex variational integrals (2011, methodology): “We refer the interested reader to [1, 13, 24, 25, 26, 28, 38, 39] and the references therein.”