ScholarLens Back to search
1998•Proceedings of the Edinburgh Mathematical SocietyOpen access

Hypoelliptic differential operators with generalized constant coefficients

Marko Nedeljkov, Stevan Pilipović

Open full text 7 citations

Abstract

The space of Colombeau generalized functions is used as a frame for the study of hypoellipticity of a family of differential operators whose coefficients depend on a small parameter ε. There are given necessary and sufficient conditions for the hypoellipticity of a family of differential operators with constant coefficients which depend on ε and behave like powers of ε as ε→0. The solutions of such family of equations should also satisfy the power order estimate with respect to ε.

Open-access reader

About this research paper

What this paper is about

The space of Colombeau generalized functions is used as a frame for the study of hypoellipticity of a family of differential operators whose coefficients depend on a small parameter ε. There are given necessary and sufficient conditions for the hypoellipticity of a family of differential operators with constant coefficients which depend on ε and behave like powers of ε as ε→0. The solutions of such family of equations should also satisfy the power order estimate with respect to ε.

Why it matters

OpenAlex reports 7 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

The space of Colombeau generalized functions is used as a frame for the study of hypoellipticity of a family of differential operators whose coefficients depend on a small parameter ε. There are given necessary and sufficient conditions for the hypoellipticity of a family of differential operators with constant coefficients which depend on ε and behave like powers of ε as ε→0. The solutions of such family of equations should also satisfy the power order estimate with respect to ε.

Key concepts: Constant coefficients, Mathematics, Differential operator, Hypoelliptic operator, Constant (computer programming), Mathematical analysis, Space (punctuation), Microlocal analysis

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
Hypoelliptic differential operators with generalized constant coefficients — Research Paper | ScholarLens