Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0793.35021
Alessandrini, G.; Magnanini, R.
The index of isolated critical points and solutions of elliptic equations in the plane. (English)
[J] Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 19, No.4, 567-589 (1992). ISSN 0391-173X

The purpose of the present paper is to point out how statements about geometric quantities associated with solutions of elliptic equations can be derived from basic facts of differential topology like index calculus and the Gauss-Bonnet theorem. We will focus on two-dimensional problems. The results we obtain are of two different kinds. (1) Identities or estimates relating the number and character of critical points (i.e., zeroes of the gradient) of solutions of elliptic equations with the boundary data. (2) Differential identities on the gradient length and the curvatures of the level curves and of the curves of steepest descent of an arbitrary smooth function with isolated critical points.

MSC 2000:: *35J05 Laplace equation, etc.
35J15 Second order elliptic equations, general
35B05 General behavior of solutions of PDE
35J25 Second order elliptic equations, boundary value problems

Keywords: index calculus; Gauss-Bonnet theorem; number and character of critical points; gradient length and the curvatures of the level curves

Cited in: Zbl 1041.81048

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Article Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]