On the local solvability of elliptic equations on compact manifolds
type: Item
instance of: scholarly article
title: On the local solvability of elliptic equations on compact manifolds
zbMATH Open document ID: 1154.58008
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 2008-11-18T00:00:00Z
review text: The interesting paper under review deals with local solvability of nonlinear elliptic equations over compact manifolds. Precisely, the local image of a nonlinear elliptic operator over a compact manifold is a submanifold described by a full set of independent equations if and only if the corank of the linearized operator is constant. In case this is not verified, the author exhibits a higher order infinitesimal invariant, the epidimension, which forces the number of independent equations to decrease. It is shown that the epidimension of a natural operator with enough symmetry must either vanish or be maximal in which case the local image admits no equation. Moreover, it is shown that, in general, a local nonlinear version of the Fredholm scheme, which always exists, encodes the maximal number of independent equations. Finally, the underdetermined elliptic case is discussed and a conjecture for it is stated.
reviewed by: Dian K. Palagachev
Mathematics Subject Classification ID: 58J05
Mathematics Subject Classification ID: 58K05
zbMATH DE Number: 5368313
zbMATH Keywords: Nonlinear elliptic operator
zbMATH Keywords: Codimension
zbMATH Keywords: Local image
zbMATH Keywords: Maximal constraints
zbMATH Keywords: Local Fredholm resolution
author: Philippe P. Delanoë
MaRDI profile type: Publication
full work available at URL: j.matpur.2008.06.007
OpenAlex ID: W2026263472
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DOI: 10.1016/J.MATPUR.2008.06.007
description: scientific article; zbMATH DE number 5368313