2023/02/07 by Tomáš Roskovec, Roskovec, Tomáš G., Filip Soudský +1
Mathematics · Computer Science · #Mathematical and Theoretical Analysis #Functional Equations Stability Results #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2302.03489
The weak lower semicontinuity of the functional F(u)=∫Ωf(x,u,∇ u) dx is a classical topic that was studied thoroughly. It was shown that if the function f is continuous and convex in the last variable, the functional is sequentially weakly lower semicontinuous on W1,p(Ω). However, the known proofs use advanced instruments of real and functional analysis. Our aim here is to present proof that can be easily understood by students familiar only with the elementary measure theory.