Pseudodifferential boundary problems and applications. (English) Zbl 0873.35117

Grubb, G.

Jahresber. Dtsch. Math.-Ver. 99, No. 3, 110-121 (1997).

In this lecture we start by recalling the features of a fundamental tool in analysis: the Fourier transformation. This tool is necessary for the following explanation of the mechanisms of pseudodifferential operators. Later in the talk we go on to more recent research results trying to give just a glimpse of what can be achieved. Plan of the talk: 1) The Fourier transformation. 2) Pseudodifferential operators. 3) Boundary value problems. 4) Parameter-dependent calculi and applications.

MSC:

35S15	Boundary value problems for PDEs with pseudodifferential operators
35-02	Research exposition (monographs, survey articles) pertaining to partial differential equations

Keywords:

pseudodifferential operators; boundary value problems; parameter-dependent calculi; Fourier transformation