ScholarLens Back to search
1995•Unpublished venueRequires access

Local Invertibility Of Sobolev Functions And Applications

Irene Fonseca, Wilfrid Gangbo

Open publisher page 0 citations

Abstract

Abstract In this chapter we show that w1,Nfunctions with positive jacobian are locally invertible, with inverse in W1,1 (see Theorem 6.1). Under suitable growth hypotheses, we are able to improve the regularity of the inverse function to W1s for some s > 1. In addition, we give a necessary condition for Sobolev functions to be invertible.

About this research paper

What this paper is about

Abstract In this chapter we show that w1,Nfunctions with positive jacobian are locally invertible, with inverse in W1,1 (see Theorem 6.1). Under suitable growth hypotheses, we are able to improve the regularity of the inverse function to W1s for some s > 1. In addition, we give a necessary condition for Sobolev functions to be invertible.

Why it matters

A significance statement is not available in the OpenAlex record.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

Abstract In this chapter we show that w1,Nfunctions with positive jacobian are locally invertible, with inverse in W1,1 (see Theorem 6.1). Under suitable growth hypotheses, we are able to improve the regularity of the inverse function to W1s for some s > 1. In addition, we give a necessary condition for Sobolev functions to be invertible.

Key concepts: Invertible matrix, Sobolev space, Inverse, Jacobian matrix and determinant, Mathematics, Pure mathematics, Inverse function, Function (biology)

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
Local Invertibility Of Sobolev Functions And Applications — Research Paper | ScholarLens