Relaxation of functionals with constraints on the divergence
Copyright policy )Relaxation of functionals with constraints on the divergence
A relaxation theorem for the functional \[ F(u)=\begin{cases}\int_\pi f(x,u(x),Du(x))dx&\quad\text{if }u\in H^{1,p}(\pi)\text{ and } div u=0\\ +\infty &\quad\text{otherwise}\end{cases} \] is proved by using the relaxation result of \textit{E. Acerbi} and \textit{N. Fusco} [Arch. Ration. Mech. Anal. 86, 125-145 (1984; Zbl 0565.49010)] on some functionals with everywhere finite integrands which approximate F(u) and by using general results in \(\Gamma\)-convergence to pass to the limit.
Methods involving semicontinuity and convergence; relaxation, relaxation theorem, Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.), gamma convergence
Methods involving semicontinuity and convergence; relaxation, relaxation theorem, Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.), gamma convergence
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