Download PDF by Molk J. (ed.): Encyclopedie des sciences mathematiques. Geometrie

By Molk J. (ed.)

ISBN-10: 2876471116

ISBN-13: 9782876471115

Show description

Read or Download Encyclopedie des sciences mathematiques. Geometrie descriptive et elementaire PDF

Best geometry and topology books

Mirrors, Prisms and Lenses. A Textbook of Geometrical Optics by J P C Southall PDF

The outgrowth of a process lectures on optics given in Columbia collage. .. In a definite feel it can be regarded as an abridgment of my treatise at the rules and strategies of geometrical optics

Glimpses of Algebra and Geometry, Second Edition - download pdf or read online

Earlier version offered 2000 copies in three years; Explores the sophisticated connections among quantity idea, Classical Geometry and sleek Algebra; Over a hundred and eighty illustrations, in addition to textual content and Maple documents, can be found through the net facilitate knowing: http://mathsgi01. rutgers. edu/cgi-bin/wrap/gtoth/; comprises an insert with 4-color illustrations; comprises a number of examples and worked-out difficulties

Extra resources for Encyclopedie des sciences mathematiques. Geometrie descriptive et elementaire

Example text

4, A∇uN · ∇ψ − f ′ (u)uN ψ dx 0 = φ2 uN 2φ A∇uN · ∇φ − dx A∇uN · ∇uN − f ′ (u)φ2 uN + ǫ (uN + ǫ)2 uN + ǫ uN dx . 1). 2. Degenerate examples. Our scope is now to show by examples that interesting degenerate cases are covered by our setting. This part is not used in the proofs of the main results, and it may thus be skipped by the uninterested reader. 2. Let p > 2. Then, there exist w ∈ C 2 (RN ) and f ∈ C 1 (R) in such a way that • w is a stable solution of ∆p w + f (w) = 0 having one-dimensional symmetry, • 0 ≤ w(x) ≤ 1 and ∂xN w(x) ≥ 0 for any x ∈ RN , • w(x) = 0 if xN ≤ 0 and w(x) = 1 if xN ≥ 1.

7). 10) |∇v(x)|4 λ1 (|∇v(x)|) ≤ const Ξ + |∇v(x)|2 a(|∇v(x)|) for any x ∈ RN . 11) |∇v(x)|2 |A(∇v(x))| ≤ const Ξ + |∇v(x)|2 a(|∇v(x)|) for any x ∈ RN . 12) BR \B√R Ξ + |∇v(x)|2 a(|∇v|) dx ≤ C ln R , |Y |2 as long as R is large enough. Then, given R > 0 (to be taken appropriately large in what follows) and x ∈ RN , we now define √  1 if |Y | ≤ R,  √ |) ϕR (x) := 2 ln(R/|Y if R < |Y | < R, ln R  0 if |Y | ≥ R. By construction, ϕR is a Lipschitz function and const x + v(x)∇v(x) ∇ϕR (x) = − |Y |2 ln R √ for any x ∈ RN such that R < |Y | < R.

Then, by (A1), R2 λ2 (|∇u(x)|) |∇u(x)|2 κ2 (x)ϕ2 (x) dx ≤ K R2 |∇ϕ(x)|2 dx . 6, since ∇u never vanishes, we conclude that the level sets are regular curves with vanishing curvatures, thence straight lines. ♦ References [AAC01] Giovanni Alberti, Luigi Ambrosio, and Xavier Cabr´e. On a long-standing conjecture of E. De Giorgi: symmetry in 3D for general nonlinearities and a local minimality property. Acta Appl. , 65(1-3):9–33, 2001. Special issue dedicated to Antonio Avantaggiati on the occasion of his 70th birthday.

Download PDF sample

Encyclopedie des sciences mathematiques. Geometrie descriptive et elementaire by Molk J. (ed.)


by Steven
4.5

Rated 4.02 of 5 – based on 49 votes