By David Kinderlehrer (Editor), Guido Stampacchia (Editor)

This unabridged republication of the 1980 textual content, a longtime vintage within the box, is a source for plenty of vital issues in elliptic equations and platforms and is the 1st sleek remedy of unfastened boundary difficulties. Variational inequalities (equilibrium or evolution difficulties as a rule with convex constraints) are conscientiously defined in An advent to Variational Inequalities and Their purposes. they're proven to be super helpful throughout a large choice of matters, starting from linear programming to loose boundary difficulties in partial differential equations. intriguing new parts like finance and part changes in addition to extra ancient ones like touch difficulties have all started to depend upon variational inequalities, making this ebook a need once more.

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Math. 36 (1983), 253-290, 571-594. 6. McLaughlin, D. , Modulations of KdV wavetrains, Physica 7. , Compacité par compensation, Ann. Scuola Norm. 8. Slemrod, M. , Measure-valued solutions to 3D 1 (1981), 355-363. Sup. Pisa 5 (1978), 489-507. a problem in dynamic phase transitions, to appear. 9. , Compensated compactness and applications to partial differential equations, in Research Notes in Mathematics : Nonlinear Analysis and Mechanics, Heriot-Watt Symposium, Vol. 4 (R. J. Knops, e d . ) , Pitman Press, 1979.

Sci. Paris 301 (1985), 345-348 and detailed paper to appear. 34 [12] Haï m Brezi s J. P. Bourguignon and J. P. Ezin, Scalar curvature functions in a conformai class of metrics and conformai transformations [13] (to a p p e a r ) . H. Brezis, Periodic solutions of nonlinear vibrating strings and duality principles, Bull. Amer. Math. Soc. 8_ (1983), 409-426. [14] H. Brezis, Elliptic equations with limiting Sobolev exponents - the impact of topology, Proc. Symp. 50th Anniversary of the Courant Institute, Comm.

I. H. P. Anal. Non. , 1984. 53 Oscillations and C o n c e n t r a t i o n s in S o l u t i o n s 13. Lions, P. , The concentration-compactness principle in the calculus of variations: the limit case, Rev. Mat. Iberoamer, 19 84. This research was supported in part by National Science Foundation Grant DMS-8301135. Department of Mathematics University of California Berkeley, CA 94720 The Connection Between the Navier-Stokes Equations, Dynamical Systems, and Turbulence Theory Ciprian Foias and Roger Témam jffTRQDyCTIOff A basic tenet of theoretical physics is that Nature is the complicated display of the repetitive interplay of some (mathematically) simple laws.