Calderón–Zygmund estimates and non-uniformly elliptic operators

By Maria Colombo, Giuseppe Mingione. 2016

282 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/72ecee461fc3b7e0e667b5cf81a3b044a689d78b

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

On the Regularity of Minima of Non-autonomous Functionals (2019, background): “d the Lavrentiev phenomenon does not appear [32] (see (1.14) below). When applied to the functional in (1.2), condition (1.10) amounts to require that (1.9) is satisﬁed. On the other hand, as seen in [4,16,17] for the speciﬁc functional in (1.9), considering bounded minimizers allows to improve the ”
Gradient regularity in mixed local and nonlocal problems (2022, background): “2) connect to a large family of problems featuring anisotropic operators and integrands with so-called nonstandard growth conditions [21,24,25,32,40,49], and to some other classes of anisotropic nonlocal problems [13–16,26,50].”
Hölder regularity for weak solutions to nonlocal double phase problems (2021, background): “5) and minimizers of corresponding variational integral has been exhaustively studied, see [2, 4, 11, 14, 15, 37] and references therein.”
A borderline case of Calder\'on-Zygmund estimates for non-uniformly elliptic problems (2019, methodology): “3) follows using monotonicity methods as described in [11].”
Gossez's approximation theorems in Musielak–Orlicz–Sobolev spaces (2017, background): “Problems in various types of the Musielak-Orlicz spaces are widely considered from analytical point as well, inter alia the highly modern calculus of variations deals with minimization of the variational integrals [4, 10, 11, 40]”
Double phase problems with variable growth (2018, background): “A key role is played by the method developed by Esposito, Leonetti, and Mingione [24] in order to prove the equivalence between the absence of Lavrentiev phenomenon and the extra regularity of the minimizers for unconstrained, non-autonomous variational problems.”