Direct Methods In The Calculus Of Variations

By A. Baer. 2016

1,324 citations recorded by the source corpus.

Subfields: Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c4f2e57e0b46128d4ed342157162a3afd9f5ee4c

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In Statistical and Nonlinear Physics

Citations in the corpus

Partial Regularity for BV Minimizers (2018, methodology): “We emphasize that quasiconvexity is much more general than convexity and refer to [24] for a long list of examples of nonconvex quasiconvex integrands.”
Higher Differentiability of Solutions of Elliptic Systems with Sobolev Coefficients: The Case p = n = 2 (2014, background): “3) For an exhaustive treatment of the regularity of solutions of elliptic systems under the assumptions (H0)– (H2) and (H3′), or local minimizers under the assumptions (F1)–(F4) and (F5′), we refer the interested reader to [17, 18] and the references therein.”
Higher differentiability for solutions to a class of obstacle problems (2018, neutral): “We start with the description of some elementary properties that can be found, for example, in [26].”
On a lemma of Jacques-Louis Lions and its relation to other fundamental results (2015, neutral): “When the boundary of Ω is smooth, a concise and elegant constructive proof was found by Dacorogna [18]; see also Dacorogna [19].”
Regularity for Double Phase Problems at Nearly Linear Growth (2023, methodology): “By (3.6), we can apply the by now classical regularity theory contained in [37, Chapter 8] and [55,56], therefore Mean value theorem and (5.2) imply Similarly, noting that | z | q − 1 ≤ | z | + 1 ≤ cF ( x , z ) + c by (1.11) 1 and q 3 / 2 (follows from (1.7) 1 ), we ﬁnd, using also mean value…”
Calderón–Zygmund estimates for parabolic p(x,t)-Laplacian systems (2014, background): “Preliminaries The following lemma is a standard iteration lemma and can be found for instance in [23], Lemma 6.”
Besov regularity for solutions of p-harmonic equations (2017, background): “We start with the description of some elementary properties that can be found, for example, in [10].”
Harnack inequalities for double phase functionals (2015, methodology): “In the standard case p = q the functional in question has standard p-polynomial growth and the regularity theory of minimisers is by now well-understood; see for instance [26, 19, 29].”