Problemes aux limites non homogenes et applications. Volume by Lions J.L., Magenes E.

By Lions J.L., Magenes E.

Show description

By Lions J.L., Magenes E.

Show description

Read Online or Download Problemes aux limites non homogenes et applications. Volume 1 PDF

Similar french_1 books

Foucault, Deleuze, Althusser & Marx

Ce livre met au jour los angeles politique dans los angeles philosophie de Foucault, Deleuze et Althusser. Foucault, l’artificier, joue un rôle décisif dans l. a. disqualification de Marx et du marxisme. Ce dommage collatéral est au cœur de son oeuvre. l. a. micropolitique subversive de Deleuze, le réfractaire, posée comme replacement au marxisme devient critique du militantisme et de l’engagement.

Additional resources for Problemes aux limites non homogenes et applications. Volume 1

Sample text

E. a map of the form (x1 , . . , xn ) → (F1 (x1 , . . , xn ), . . , Fn (x1 , . . , xn )) where each Fi ∈ ‫[ރ‬X] := ‫[ރ‬X1 , . . , Xn ], the n variable polynomial ring over ‫ރ‬. Furthermore for z ∈ ‫ރ‬n put F (z) := det(JF (z)) where JF = ∂Fi ∂Xj 1≤i,j≤n is the Jacobian matrix over F . 2 — Let F (a) = F (b) for some a, b ∈ ‫ރ‬n with a = b. Does it follow that F (z) = 0 for some z ∈ ‫ރ‬n . The answer (at this moment) is: we don’t know if n ≥ 2! In fact this question is, as we will show below, a reformulation of the famous Jacobian Conjecture.

Ym ) is a product of elementary polynomial maps). 13 (Lang, Maslamani, [39]) — Let k be a field with char(k) = 0 and let F1 , . . , Fn ∈ k[X] with det(JF ) ∈ k ∗ . 1. If Fi ∈ Xi k[X] for all i, then Fi = λi Xi with λi ∈ k ∗ , so F is invertible. 2. If Fi = Xi + λi Mi for all i, where λi ∈ k and Mi is a monomial, then F is invertible. 1 Derivations and the Jacobian Condition The aim of this section is to study the Jacobian Conjecture by means of derivations. Therefore we first reformulate the Jacobian Conjecture in terms of the kernel of a special derivation.

In fact he completely classified all maps of the form (1) satisfying det(JF ) = 1. 8 (Hubbers, [31]) — Let F = X − H be a cubic homogeneous polynomial map in dimension four, such that det(JF ) = 1. Then there exists some T ∈ GL4 (‫)ރ‬ with T −1 ◦ F ◦ T being one of the following forms:   x1     x2     1.  x3     x −a x3 − b x2 x − c x2 x − e x x2 − f x x x  4 1 4 1 2 4 1 3 4 1 2 4 1 2 3   4 −h4 x1 x23 − k4 x32 − l4 x22 x3 − n4 x2 x23 − q4 x33 Séminaires et Congrès 2 59 Polynomial Automorphisms and the Jacobian Conjecture  x1   x2 2.

Download PDF sample

Rated 4.31 of 5 – based on 33 votes