Microlocal hypoellipticity of linear partial differential operators with generalized functions as coefficients

By G. Hörmann, Michael Oberguggenberger, Stevan Pilipovic. 2003

77 citations recorded by the source corpus.

We investigate microlocal properties of partial differential operators with generalized functions as coefficients. The main result is an extension of a corresponding (microlocalized) distribution theoretic result on operators with smooth hypoelliptic symbols. Methodological novelties and technical refinements appear embedded into classical strategies of proof in order to cope with most delicate interferences by non-smooth lower order terms. We include simplified conditions which are applicable in special cases of interest.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/955872ec348fff706a129bbead93cd8ca2886de4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Claudia Garetto
2. Todor Gramchev
3. Michael Oberguggenberger
4. G. Hörmann

In Mathematical Physics

1. Claudia Garetto
2. Todor Gramchev
3. Michael Oberguggenberger
4. G. Hörmann

Citations in the corpus

• MICROLOCAL ANALYSIS OF GENERALIZED FUNCTIONS: PSEUDODIFFERENTIAL TECHNIQUES AND PROPAGATION OF SINGULARITIES (2004, methodology): “[18, 14, 13, 16, 12, 6, 7]).”
• Pseudodifferential operators with generalized symbols and regularity theory (2005, background): “These effects and a regularity theory for such operators was developed in [24], see also [31], and extended to the case of partial differential operators with generalized, non-constant coefficients in [25].”
• Elliptic regularity and solvability for partial differential equations with Colombeau coefficients (2003, background): “The general case of higher order equations with non-constant generalized coefficients remains open and will be addressed in [11].”