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

Agnieszka 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 -