Regularity results for minimizers of irregular integrals with (p,q) growth

By L. Esposito, Francesco Leonetti, Giuseppe Mingione. 2002

128 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/fdf8538d184ab391b84473de76f54c8e0f14375c

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In Applied Mathematics

In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

On the Regularity of Minima of Non-autonomous Functionals (2019, methodology): “et signiﬁcant problem; i.e., we take functionals with (p,q)-growth as in (1.1), with Lipschitz dependence on x, and in the nondegenerate case λ = 1. This is for instance the setting of [43], see also [31,32]. More in general, non-polynomial growth settings, can be considered too. Speciﬁcally, we con”
Higher differentiability of minimizers of convex variational integrals (2011, methodology): “While aspects of our proof in this case are similar to that of [14] our approach via higher order singular perturbations appears less involved.”
The Singular Set of ω-minima (2005, methodology): “we can use ϕ as a test map in (3.17) (see [ 9 ], Lemma 4.1 for details).”
Gradient estimates below the duality exponent (2010, unknown): “With s = 0 and c(·, ·) ≡ 1 we indeed recover the p-Laplacean operator [47],[49],[50],[28],[29], that is −4pu = −div(|Du|p−2Du) = f .”
Global regularity for almost minimizers of nonconvex variational problems (2008, background): “[8] and Marcellini and Papi [20] have extended Uhlenbeck’s work to allow much flexibility in the way the integrand may grow.”
The Calderón-Zygmund theory for elliptic problems with measure data (2006, methodology): “Moreover, in order to apply the technique of [29] we also need a technical assumption, namely we need to take φ such that ∫ B1\B1/2 φ(z) dz ≥ 1/1000 .”
Regularity of minimizers of autonomous convex variational integrals (2013, background): “We remark that under the assumptions (H1), (H2) on the integrand F the W1,2 loc higher differentiability of V (Du) has previously been established only when the exponents p, q satisfy the stronger conditions 1 < p  q < n+1 n p, see [8], and also [2,3,7,9,10].”
Lipschitz estimates for systems with ellipticity conditions at infinity (2016, methodology): “Since D2 f has p − 2 growth, by using the technique of the difference quotients (see for example [14,19,23]), we have that”
Potential estimates and gradient boundedness for nonlinear parabolic systems (2012, methodology): “Then aε(·) is clearly a smooth vector field and, moreover, the following structural conditions hold: ⎨⎩|aε(z)|+ |∂aε(z)| (|z|2 + s2ε)1/2 ≤ c (|z|2 + s2ε)(p−1)/2 , c−1 (|z|2 + s2ε)(p−2)/2 |λ|2 ≤ 〈∂aε(z)λ, λ〉 whenever z, λ ∈ R, with a constant c ≥ 1 depending only n, p, ν, L but not on ε; for this see”
Regularity of minimizers of vectorial integrals with p − q growth (2003, background): “1 in [5] to non-homogeneous energy densities, with a similar proof that we omit.”