Nonconvex Minimization Problems for Functionals Defined on Vector Valued Functions

Crasta, Graziano; Malusa, Annalisa

doi:10.1006/jmaa.2000.7227

Cited by 7 publications

(7 citation statements)

References 17 publications

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“…Since the set {(f * * ) (ξ); ξ ∈ R} is the open interval ] − 1, 1[, it is clear that (9) cannot be satisfied if T > N (we recall that, in this case, we can choose M ∈]0, 1[ in (H2)). On the other hand, if T = N , from (9) we deduce that φ (t) = N 2 /(4t 2 ), but in this case φ does not belong to K α .…”

Section: Notation and Statement Of The Resultsmentioning

confidence: 99%

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On the existence and uniqueness of minimizers for a class of integral functionals

Crasta¹,

Malusa²

2005

Nonlinear differ. equ. appl.

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We study the solvability of the minimization problem \[ \min_{\eta \in\Kd} \int_0^T \alpha(t)[f(|\eta'(t)|)+g(\eta(t))]\, dt\,, \] where $\Kd$ is a subset of $AC_{loc}[0,T[$ depending on the weight function $\alpha$. Neither the convexity nor the superlinearity of $f$ are required. The main application concerns the existence and uniqueness of minimizers to integral functionals on convex domains $\Omega \subset \R^{N}$, defined in the class of functions in $\Wuu (\Omega)$ depending only on the distance from the boundary of $\Omega$. As a corollary, when $\Omega$ is a ball we obtain the existence of radially symmetric solutions to nonconvex and noncoercive functionals

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Section: Notation and Statement Of The Resultsmentioning

confidence: 99%

“…In particular, if Ω is a ball centered at the origin, we recover the sufficient conditions for the existence and uniqueness of a radially symmetric solution to (6) proved in [8,9].…”

Section: Introductionmentioning

confidence: 99%

On the existence and uniqueness of minimizers for a class of integral functionals

Crasta¹,

Malusa²

2005

Nonlinear differ. equ. appl.

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“…Under these assumptions, in [5] it is proved that the function u 0 provides a solution to (13), and the proof of Theorem 2.1 can be carried out in the very same way.…”

Section: Theorem 23 Assume That F Satisfies (H1-h3) and In Additimentioning

confidence: 99%

“…For this reason, a branch of the recent developments in the theory of Calculus of Variations is devoted to the study of such "nonstandard problems". Among others, we mention [8,14,18] and the references therein (see also [9][10][11][12][13] for radially symmetric problems). The result presented in this paper fits into the framework introduced by Cellina in [8], and developed in [6,7,20,21].…”

Section: Introductionmentioning

confidence: 99%

Geometric constraints on the domain for a class of minimum problems

Crasta

Malusa

2003

ESAIM: COCV

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“…When W is a ball of radius R, then it is well known (see [5][6][7][8][9]) that the functional J admits a unique (radially symmetric) minimizer in W 0 (W) and the equality holds in (4).…”

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confidence: 99%