Lower semicontinuity of multiple $\sf \mu $-quasiconvex integrals

Ilaria Fragalà

Displaying similar documents to “Lower semicontinuity of multiple $μ$ -quasiconvex integrals”

The Euler equation for a class of nonconvex problems.

Buttazzo, Giuseppe, Faina, Loris (1994)

Portugaliae Mathematica

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Product of vector measures on topological spaces

Surjit Singh Khurana (2008)

Commentationes Mathematicae Universitatis Carolinae

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For $i = (1, 2)$ , let $X_{i}$ be completely regular Hausdorff spaces, $E_{i}$ quasi-complete locally convex spaces, $E = E_{1} \overset{˘}{\otimes} E_{2}$ , the completion of the their injective tensor product, $C_{b} (X_{i})$ the spaces of all bounded, scalar-valued continuous functions on $X_{i}$ , and $μ_{i}$ $E_{i}$ -valued Baire measures on $X_{i}$ . Under certain conditions we determine the existence of the $E$ -valued product measure $μ_{1} \otimes μ_{2}$ and prove some properties of these measures.

Potential theory of quasiminimizers.

Kinnunen, Juha, Martio, Olli (2003)

Annales Academiae Scientiarum Fennicae. Mathematica

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Integral and derivative operators of functional order on generalized Besov and Triebel-Lizorkin spaces in the setting of spaces of homogeneous type

Silvia I. Hartzstein, Beatriz E. Viviani (2002)

Commentationes Mathematicae Universitatis Carolinae

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In the setting of spaces of homogeneous-type, we define the Integral, $I_{φ}$ , and Derivative, $D_{φ}$ , operators of order $φ$ , where $φ$ is a function of positive lower type and upper type less than $1$ , and show that $I_{φ}$ and $D_{φ}$ are bounded from Lipschitz spaces $Λ^{ξ}$ to $Λ^{ξ φ}$ and $Λ^{ξ / φ}$ respectively, with suitable restrictions on the quasi-increasing function $ξ$ in each case. We also prove that $I_{φ}$ and $D_{φ}$ are bounded from the generalized Besov ${\dot{B}}_{p}^{ψ, q}$ , with $1 \leq p, q < \infty$ , and Triebel-Lizorkin spaces ${\dot{F}}_{p}^{ψ, q}$ , with $1 < p, q < \infty$ , of order $ψ$ to those of order...

Dichotomies for $𝐂_{0} (X)$ and $𝐂_{b} (X)$ spaces

Szymon Głąb, Filip Strobin (2013)

Czechoslovak Mathematical Journal

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Jachymski showed that the set $\{(x, y) \in 𝐜_{0} \times 𝐜_{0} : {(\sum_{i = 1}^{n} α (i) x (i) y (i))}_{n = 1}^{\infty} is bounded\}$ is either a meager subset of $𝐜_{0} \times 𝐜_{0}$ or is equal to $𝐜_{0} \times 𝐜_{0}$ . In the paper we generalize this result by considering more general spaces than $𝐜_{0}$ , namely $𝐂_{0} (X)$ , the space of all continuous functions which vanish at infinity, and $𝐂_{b} (X)$ , the space of all continuous bounded functions. Moreover, we replace the meagerness by $σ$ -porosity.

An optimal matching problem

Ivar Ekeland (2005)

ESAIM: Control, Optimisation and Calculus of Variations

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Given two measured spaces $(X, μ)$ and $(Y, ν)$ , and a third space $Z$ , given two functions $u (x, z)$ and $v (x, z)$ , we study the problem of finding two maps $s : X \to Z$ and $t : Y \to Z$ such that the images $s (μ)$ and $t (ν)$ coincide, and the integral $\int_{X} u (x, s (x)) d μ - \int_{Y} v (y, t (y)) d ν$ is maximal. We give condition on $u$ and $v$ for which there is a unique solution.

Displaying similar documents to “Lower semicontinuity of multiple μ -quasiconvex integrals”

The Euler equation for a class of nonconvex problems.

Product of vector measures on topological spaces

Potential theory of quasiminimizers.

Integral and derivative operators of functional order on generalized Besov and Triebel-Lizorkin spaces in the setting of spaces of homogeneous type

Dichotomies for 𝐂 0 ( X ) and 𝐂 b ( X ) spaces

An optimal matching problem

Displaying similar documents to “Lower semicontinuity of multiple $μ$ -quasiconvex integrals”

Dichotomies for $𝐂_{0} (X)$ and $𝐂_{b} (X)$ spaces