Partial regularity for anisotropic functionals   of higher order

Menita Carozza; Antonia Passarelli di Napoli

Displaying similar documents to “Partial regularity for anisotropic functionals of higher order”

Asymptotic behaviour of a class of degenerate elliptic-parabolic operators: a unitary approach

Fabio Paronetto (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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We study the asymptotic behaviour of a sequence of strongly degenerate parabolic equations $\partial_{t} (r_{h} u) - div (a_{h} \cdot D u)$ with $r_{h} (x, t) \geq 0$ , $r_{h} \in L^{\infty} (Ω \times (0, T))$ . The main problem is the lack of compactness, by-passed via a regularity result. As particular cases, we obtain -convergence for elliptic operators $(r_{h} \equiv 0)$ , -convergence for parabolic operators $(r_{h} \equiv 1)$ , singular perturbations of an elliptic operator $(a_{h} \equiv a$ and $r_{h} \to r$ , possibly $r \equiv 0)$ .

On the lower semicontinuity of supremal functionals

Michele Gori, Francesco Maggi (2003)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we study the lower semicontinuity problem for a supremal functional of the form $F (u, Ω) = \underset{x \in Ω}{ess \sup} f (x, u (x), D u (x))$ with respect to the strong convergence in $L^{\infty} (Ω)$ , furnishing a comparison with the analogous theory developed by Serrin for integrals. A sort of Mazur’s lemma for gradients of uniformly converging sequences is proved.

Model problems from nonlinear elasticity: partial regularity results

Menita Carozza, Antonia Passarelli di Napoli (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we prove that every weak and strong local minimizer $u \in W^{1, 2} (Ω, ℝ^{3})$ of the functional $I (u) = \int_{Ω} {| D u |}^{2} + f (Adj D u) + g (\det D u),$ where $u : Ω \subset ℝ^{3} \to ℝ^{3}$ , grows like ${| Adj D u |}^{p}$ , grows like ${| \det D u |}^{q}$ and , is $C^{1, α}$ on an open subset $Ω_{0}$ of such that $𝑚𝑒𝑎𝑠 (Ω ∖ Ω_{0}) = 0$ . Such functionals naturally arise from nonlinear elasticity problems. The key point in order to obtain the partial regularity result is to establish an energy estimate of Caccioppoli type, which is based on an appropriate choice of the test functions. The limit case $p = q \leq 2$ is also treated for weak local minimizers. ...

Finite element analysis of the Signorini problem

Jaroslav Haslinger (1979)

Commentationes Mathematicae Universitatis Carolinae

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On the minimization of some nonconvex double obstacle problems.

Elfanni, A. (2003)

Journal of Applied Mathematics

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Partial regularity of solution to generalized Navier-Stokes problem

Václav Mácha (2014)

Open Mathematics

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In the presented work, we study the regularity of solutions to the generalized Navier-Stokes problem up to a C 2 boundary in dimensions two and three. The point of our generalization is an assumption that a deviatoric part of a stress tensor depends on a shear rate and on a pressure. We focus on estimates of the Hausdorff measure of a singular set which is defined as a complement of a set where a solution is Hölder continuous. We use so-called indirect approach to show partial regularity,...

Stability results for obstacle problems with measure data

Chiara Leone (2005)

Annales de l'I.H.P. Analyse non linéaire

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