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

• Autorzy: Agnieszka Kałamajska
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 49J45: Methods involving semicontinuity and convergence; relaxation
• 35E10: Convexity properties

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2001
• Tom: 89
• Numer: 1
• Strony: 43-59

Daty

wydano

2001

Twórcy

autor

Agnieszka Kałamajska

• Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland

Identyfikatory

DOI

10.4064/cm89-1-3