Microlocal defect measures
- 1 January 1991
- journal article
- research article
- Published by Taylor & Francis in Communications in Partial Differential Equations
- Vol. 16 (11) , 1761-1794
- https://doi.org/10.1080/03605309108820822
Abstract
In order to study weak continuity of quadratic forms on spaces of L2 solutions of systems of partial differential equations, we define defect measures on the space of positions and frequencies.A systematic use of these measures leads in particular to a compensated compactness theorem, generalizing MURAT"TARTAR's compensated compactness to variable coefficients and GOLSE"LIONS"PERTHAME"SENTIS's averaging lemma. We also obtain results on homogenization for differential operators of order I with oscillating coefficients.Keywords
This publication has 6 references indexed in Scilit:
- Moyennisation et régularité deux-microlocaleAnnales Scientifiques de lʼÉcole Normale Supérieure, 1990
- Global weak solutions of Vlasov‐Maxwell systemsCommunications on Pure and Applied Mathematics, 1989
- Regularity of the moments of the solution of a Transport EquationJournal of Functional Analysis, 1988
- The Concentration-Compactness Principle in the Calculus of Variations. The limit case, Part 1Revista Matemática Iberoamericana, 1985
- Applications bilineaires compatibles avec un systeme a coefficients variables continuite dans les espaces de besov.Communications in Partial Differential Equations, 1985
- On the propagation of polarization sets for systems of real principal typeJournal of Functional Analysis, 1982