ScholarLens Back to search
1993•Mathematische NachrichtenRequires access

Pseudodifferential Operators on Compact Manifolds with Lipschitz Boundary

Roland Duduchava, Frank‐Olme Speck

Open publisher page 42 citations

Abstract

Abstract Pseudodifferential operators with non‐smooth symbols on a manifold M with Lipschitz boundary are considered. Theorems about order reduction and localization of such operators in Bessel potential H and Hölder‐Zygmund Z(IR n ) spaces are proved. A pseudodifferential operator A with locally sectorial matrix symbol is proved to be Fredholm in the space H ( M ) and Ind A = 0 where s depends on A. Application to a boundary value problem for an elastic body with crack is discussed in conclusion.

About this research paper

What this paper is about

Abstract Pseudodifferential operators with non‐smooth symbols on a manifold M with Lipschitz boundary are considered. Theorems about order reduction and localization of such operators in Bessel potential H and Hölder‐Zygmund Z(IR n ) spaces are proved. A pseudodifferential operator A with locally sectorial matrix symbol is proved to be Fredholm in the space H ( M ) and Ind A = 0 where s depends on A. Application to a boundary value problem for an elastic body with crack is discussed in conclusion.

Why it matters

OpenAlex reports 42 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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 Pseudodifferential operators with non‐smooth symbols on a manifold M with Lipschitz boundary are considered. Theorems about order reduction and localization of such operators in Bessel potential H and Hölder‐Zygmund Z(IR n ) spaces are proved. A pseudodifferential operator A with locally sectorial matrix symbol is proved to be Fredholm in the space H ( M ) and Ind A = 0 where s depends on A. Application to a boundary value problem for an elastic body with crack is discussed in conclusion.

Key concepts: Mathematics, Pseudodifferential operators, Lipschitz continuity, Bessel function, Boundary (topology), Mathematical analysis, Manifold (fluid mechanics), Pure mathematics

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
Pseudodifferential Operators on Compact Manifolds with Lipschitz Boundary — Research Paper | ScholarLens