Regularity results for vectorial minimizers of a class of degenerate convex integrals

Cupini, Giovanni; Giannetti, Flavia; Giova, Raffaella; Napoli, Antonia Passarelli di

doi:10.1016/j.jde.2018.06.010

Cited by 39 publications

(20 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Now we conclude the proof by passing to the limit in the approximating problem. The limit procedure is standard (see for example [11]) and we just give here a brief sketch. Let u ∈ K ψ (Ω) be a solution to (1.1) and let F ε be the sequence obtained applying Lemma 2.3 to the integrand F .…”

Section: Proof Of Theorem 12mentioning

confidence: 99%

“…We conclude mentioning that condition (1.5) is sharp also to obtain the Lipschitz continuity of solutions to elliptic equations and systems and minimizers of related functionals with p, q−growth (see [20][21][22]) and can be framed into the research concerning regularity results under non standard growth conditions, that, after the pioneering papers by Marcellini [35][36][37] has attracted growing attention, see among the others [3,10,11,19,32,38,43].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Regularity results for a class of obstacle problems with p, q−growth conditions

2021

Self Cite

View full text Add to dashboard Cite

In this paper we prove the the local Lipschitz continuity for solutions to a class of obstacle problems of the type[[EQUATION]] Here $\mathcal{K}_{\psi}(\Omega)$ is the set of admissible functions $z \in {u_0 + W^{1,p}(\Omega)}$ {for a given $u_0 \in W^{1,p}(\Omega)$}such that $z \ge \psi$ a.e. in $\Omega$, $\psi$ being the obstacle and $\Omega$ being an open bounded set of $\mathbb{R}^n$, $n \ge 2$.The main novelty here is that we are assuming that the integrand $ F(x, Dz)$ satisfies $(p,q)$-growth conditions and as a function of the $x$-variable belongs to a suitable Sobolev class. We remark that the Lipschitz continuity result is obtained under a sharp closeness condition between the growth and the ellipticity exponents.Moreover, we impose lessrestrictive assumptions on the obstacle with respect to the previous regularity results.Furthermore, assuming the obstacle $\psi$ is locally bounded, we prove the local boundedness of the solutions to a quite large class of variational inequalities whose principal part satisfies non standard growthconditions.

show abstract

Section: Proof Of Theorem 12mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Regularity results for a class of obstacle problems with p, q−growth conditions

2021

Self Cite

View full text Add to dashboard Cite

show abstract

“…In the case of p ‐Laplace type systems with coefficients that are not differentiable, but merely Hölder continuous, Mingione [29, 30] proved a fractional higher differentiability result in the sense that the gradient of solutions still belongs to a fractional Sobolev space, and applied this result to derive a dimension estimate for the singular set of solutions. On the other hand, in [33, 34] the second author observed that solutions admit a full additional derivative in the sense of

V_{μ} false(D u false) \in W_{normalloc}^{1, 2} false(normalΩ false)

if the coefficients only possess a Sobolev type regularity, see also [12, 20, 21, 23]. Finally, both types of results were unified in [3, 11], where a fractional differentiability result in the scale of Besov spaces was established under the assumption that the coefficients admit a Besov‐type regularity property.…”

Section: Introductionmentioning

confidence: 99%

Higher differentiability for solutions of stationary p‐Stokes systems

Giannetti

Napoli

Scheven

2020

Mathematische Nachrichten

Self Cite

View full text Add to dashboard Cite

We consider weak solutions (,) ∶ Ω → ℝ × ℝ to stationary-Stokes systems of the type { −div (, ) + ∇ + [ ] = , div = 0 in Ω ⊂ ℝ , where the function (,) satisfies-growth conditions in and depends Hölder continuously on. By  we denote the symmetric part of the gradient and we write [ ] for the convective term. In this setting, we establish results on the fractional higher differentiability of both the symmetric part of the gradient  and of the pressure. As an application, we deduce dimension estimates for the singular set of the gradient , thereby improving known results on partial 1,-regularity for solutions to stationary-Stokes systems.

show abstract

“…In a series of papers, Baroni, Colombo and Mingione [3,5,16,17,18] have studied regularity properties of minimizers of these problems, see also [9,46]. Other researchers [15,21] have considered the variant of the double phase functional, F (x, t) ≈ (t − 1) p − + a(x)(t − 1) q − , with (s) − := max{s, 0}, which is degenerate for positive values of the gradient. Furthermore, minimizers of borderline functionals like F (x, t) = t p(x) log(e + t) or F (x, t) = t p + a(x)t p log(e + t) have been recently studied, see for instance [4,9,24,44,45,47].…”

Section: Introductionmentioning

confidence: 99%

Calderón–Zygmund estimates in generalized Orlicz spaces

Hästö

2019

Journal of Differential Equations

View full text Add to dashboard Cite

We establish the W 2,ϕ(•) -solvability of the linear elliptic equations in nondivergence form under a suitable, essentially minimal, condition of the generalized Orlicz function ϕ(•) = ϕ(x, t), by deriving Calderón-Zygmund type estimates. The class of generalized Orlicz spaces we consider here contains as special cases classical Lebesgue and Orlicz spaces, as well as non-standard growth cases like variable exponent and double phase growth.

show abstract

Regularity results for vectorial minimizers of a class of degenerate convex integrals

Cited by 39 publications

References 35 publications

Regularity results for a class of obstacle problems with p, q−growth conditions

Regularity results for a class of obstacle problems with p, q−growth conditions

Higher differentiability for solutions of stationary p‐Stokes systems

Calderón–Zygmund estimates in generalized Orlicz spaces

Contact Info

Product

Resources

About