Data: piątek, 16.12.2022, godz. 11:00-12:00
Prelegent: dr Filip Soudsky
Abstrakt: We shall recover the classical theorem about lower-semicontinuity of the functional
\[
\mathcal{F}(u):=\int_{\Omega}f(x,u,\nabla u) dx
\]
Unlike the classical proof, our proof will use only elementary measure theoretic results. First we will show the lower semi-continuity of functional
\[
J(u,v)=\int_{\Omega}f(x,u,v) dx
\]
for functions convex in last variable with respect to topology defined as a product topology of convergence in measure and the weak convergence in \(L^p\) and use this to obtain the result.
Miejsce: A1-33 (sala RND)