Analysis of Concentration and Oscillation Effects Generated by Gradients
- 1 July 1998
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Mathematical Analysis
- Vol. 29 (3) , 736-756
- https://doi.org/10.1137/s0036141096306534
Abstract
A general theorem characterizing the interaction of concentrations and oscillations effects associated with sequences of gradients bounded in Lp, t p > 1, is proved. The oscillations are recorded in the Young measure while the concentrations are encoded in the varifold.Keywords
This publication has 19 references indexed in Scilit:
- Proposed experimental tests of a theory of fine microstructure and the two-well problemPhilosophical Transactions A, 1992
- Weak Convergence Methods for Nonlinear Partial Differential EquationsPublished by American Mathematical Society (AMS) ,1990
- Oscillations and concentrations in weak solutions of the incompressible fluid equationsCommunications in Mathematical Physics, 1987
- Fine phase mixtures as minimizers of energyArchive for Rational Mechanics and Analysis, 1987
- Compensated compactness and general systems of conservation lawsTransactions of the American Mathematical Society, 1985
- Semicontinuity problems in the calculus of variationsArchive for Rational Mechanics and Analysis, 1984
- Convergence of approximate solutions to conservation lawsArchive for Rational Mechanics and Analysis, 1983
- Quasiconvexity and relaxation of nonconvex problems in the calculus of variationsJournal of Functional Analysis, 1982
- On the First Variation of a VarifoldAnnals of Mathematics, 1972
- Existence and Regularity Almost Everywhere of Solutions to Elliptic Variational Problems among Surfaces of Varying Topological Type and Singularity StructureAnnals of Mathematics, 1968