Vectorial nonlinear potential theory

By Tuomo Kuusi, Giuseppe Mingione. 2018

148 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c84db1b5cddd0698d94c74e6fd13178241eb1813

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Citations in the corpus

Recent developments in problems with nonstandard growth and nonuniform ellipticity (2021, methodology): “There is a large amount literature on such functionals, especially as far as regularity issues are concerned (see [146,162,163], and also [173] for a review).”
A borderline case of Calder\'on-Zygmund estimates for non-uniformly elliptic problems (2019, background): “Needless to say, when a(x) ≡ 0 the functional P reduces to the standard p-Laplacean functional (we refer to the papers [21, 22] for a recent update of regularity theory in the standard p-case and to [33, 34] for the beginnings).”
Lipschitz Bounds and Nonautonomous Integrals (2020, unknown): “a: (0,∞) → [0,∞) is of class C1 loc(0,∞) . A special, yet important mode is given by the p-Laplacean system with coeﬃcients (1.5) − div(c(x)|Du|p−2Du) = f, p>1, 0 <ν≤ c(·) ≤ L. For this we have [47,48] Nonlinear Stein Theorem. Let u∈ W1,p loc (Ω;R N) be a weak solution to (1.5). If f ∈ L(n,1)(”
Manifold Constrained Non-uniformly Elliptic Problems (2019, background): “espectively. Forresultsconcerning more general functionals as in (1.1) with p-growth, that is, modelled on the one in (1.2) and therefore satisfying |z|p . F(x,w,z) . |z|p +1 , (1.4) see for instance [41, 42, 45] and related references. Under suitable assumptions, the ﬁnal outcome is that minima are”
Regularity for general functionals with double phase (2017, background): “ main results of this paper, stated in the next Theorem 1.1 and 1.2, draw a complete parallel with the theory of functionals with standard polynomial growth [28, 41, 42] i.e., when a(·) ≡ 0; see also [35, 36] for more recent a priori estimates. Theorem 1.1 (Maximal regularity). Let u ∈ W1,p(Ω) be a ”
A pocket guide to nonlinear differential equations in Musielak–Orlicz spaces (2018, background): “For a full account of estimates for general elliptic equations of p-Laplace-type in the scalar case we refer to [133], while for the vectorial one to [135], whereas the corresponding results for parabolic problems are provided in [134].”
On the Regularity of Minima of Non-autonomous Functionals (2019, background): “See [40, 41, 46, 52, 53] for regularity results in this situation.”