- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:24
Portugaliae Mathematica
Port. Math.
PM
0032-5155
1662-2758
General
10.4171/PM
http://www.ems-ph.org/doi/10.4171/PM
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2008)
72
2015
2
A note on two scale compactness for $p = 1$
Laura
Bufford
Carnegie Mellon University, PITTSBURGH, UNITED STATES
Irene
Fonseca
Carnegie Mellon University, PITTSBURGH, UNITED STATES
Two-scale convergence, periodic integrals
In this paper the notion of two-scale convergence introduced by G. Nguetseng and G. Allaire is extended to the case of bounded sequences in $L^1(\Omega)$, where $\Omega$ is any open subset of $\mathbb{R}^N$. Three different approaches will be considered: an adaptation of the method used in $L^p(\Omega)$ with $p>1$, a measure-theoretic argument, and the periodic unfolding technique.
Partial differential equations
Calculus of variations and optimal control; optimization
101
117
10.4171/PM/1959
http://www.ems-ph.org/doi/10.4171/PM/1959