Titlebook: Regularity Results for Nonlinear Elliptic Systems and Applications; Alain Bensoussan,Jens Frehse Book 2002 Springer-Verlag Berlin Heidelbe

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WATER

正論

Nonlinear Elliptic Systems Arising from plasticity Theory,ment is recovered indirectly. The convergence of the approximation is very natural in the context of variational problems and follows from general penalty methods (see R. Temam [101], G. Duvaut, J.L. Lions [15], J.L. Lions [70], P. Le Tallec [69]).

lactic

闡釋

General Regularity Results,g .. and .. regularity. We shall then derive additional regularity. In the sequel everything is self-contained, except that we shall make use of the .. regularity results for the linear Dirichlet problem. For equations we rely heavily on O.A. Ladyzhenskaya, N.N. Ural’tseva [66].

Gene408

Nonlinear Elliptic Systems Arising from Stochastic Games,liptic systems, the Bellman system. The method consists in applying the dynamic programming approach. The value functions are the solutions of a system of partial differential equations. From regularity results, one is able to construct continuous feedbacks, which will represent optimal controls for

凝乳

Harmonic Mappings, of .. into the unit sphere of ... This is, however, sufficient to cover many of the analytical difficulties. There is a large litterature, starting with the famous paper of J. Eells, J.H. Sampson [22]. Let us introduce the problem: Let . be a bounded open subset of .., . ≥ 2, and . Find . such that

hankering

,Stationary Navier—Stokes Equations,n a bounded domain, where the time variable intervenes, the issue of regularity of weak solutions is an open problem in dimension . = 3 (see J. Leray [68] or O.A. Ladyzenskaya, V.A. Solonnikov, N.N. Ural’tseva [67] for the background). Only partial regularity is available; see L. Caffarelli, R. Kohn

shrill

Nonlinear Elliptic Systems Arising from plasticity Theory,o attach to tensor . its deviator . which has trace 0. We will consider two models of plasticity, the Hencky model, which is a model of perfect plasticity where, . (. is a given constant), and the Norton—Hoff model, which is an approximation to the Hencky model, where the constraint of perfect plast

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