# On the condition of Λ-convexity in some problems of weak continuity and weak lower semicontinuity

Colloquium Mathematicae (2001)

- Volume: 89, Issue: 1, page 43-59
- ISSN: 0010-1354

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topAgnieszka Kałamajska. "On the condition of Λ-convexity in some problems of weak continuity and weak lower semicontinuity." Colloquium Mathematicae 89.1 (2001): 43-59. <http://eudml.org/doc/286256>.

@article{AgnieszkaKałamajska2001,

abstract = {We study the functional $I_\{f\}(u)=∫_\{Ω\} f(u(x))dx$, where u=(u₁, ..., uₘ) and each $u_\{j\}$ is constant along some subspace $W_\{j\}$ of ℝⁿ. We show that if intersections of the $W_\{j\}$’s satisfy a certain condition then $I_\{f\}$ is weakly lower semicontinuous if and only if f is Λ-convex (see Definition 1.1 and Theorem 1.1). We also give a necessary and sufficient condition on $\{W_\{j\}\}_\{j=1,...,m\}$ to have the equivalence: $I_\{f\}$ is weakly continuous if and only if f is Λ-affine.},

author = {Agnieszka Kałamajska},

journal = {Colloquium Mathematicae},

keywords = {integral functionals; weak continuity; weak lower semicontinuity},

language = {eng},

number = {1},

pages = {43-59},

title = {On the condition of Λ-convexity in some problems of weak continuity and weak lower semicontinuity},

url = {http://eudml.org/doc/286256},

volume = {89},

year = {2001},

}

TY - JOUR

AU - Agnieszka Kałamajska

TI - On the condition of Λ-convexity in some problems of weak continuity and weak lower semicontinuity

JO - Colloquium Mathematicae

PY - 2001

VL - 89

IS - 1

SP - 43

EP - 59

AB - We study the functional $I_{f}(u)=∫_{Ω} f(u(x))dx$, where u=(u₁, ..., uₘ) and each $u_{j}$ is constant along some subspace $W_{j}$ of ℝⁿ. We show that if intersections of the $W_{j}$’s satisfy a certain condition then $I_{f}$ is weakly lower semicontinuous if and only if f is Λ-convex (see Definition 1.1 and Theorem 1.1). We also give a necessary and sufficient condition on ${W_{j}}_{j=1,...,m}$ to have the equivalence: $I_{f}$ is weakly continuous if and only if f is Λ-affine.

LA - eng

KW - integral functionals; weak continuity; weak lower semicontinuity

UR - http://eudml.org/doc/286256

ER -

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