Contents/conteúdo

Mathematics Department Técnico Técnico

Colloquium  RSS

21/09/2000, 16:30 — 17:30 — Amphitheatre Pa1, Mathematics Building
, Linköpings Universitet

Some Open Problems in Partial Differential Equations

The development of the theory of elliptic boundary value problems in the last century is concentrated mainly around the 19th and 20th Hilbert problems, dealing with existence, analyticity, and regularity properties of solutions. It is believed that both problems have been principally solved.

I intend to show that Hilbert’s program is far from being exhausted and still is able to give strong impetus to the theory of elliptic equations. Among the deep problems which are waiting to be explored are:

  1. Description of classes of elliptic systems as well as higher order elliptic equations and variational problems with analytic nonlinearities which have only analytic solutions.
  2. Characterization of local and boundary singularities of nonlinear elliptic equations.
  3. The study of boundary behaviour of solutions to nonlinear and higher order linear equations in domains with unrestricted boundaries. In particular, a circle of questions concentrated around Wiener’s criterion for regularity of a boundary point.

link

Colloquium_logo

The Mathematics Colloquium is a series of monthly talks organized by the Department of Mathematics of IST, aiming to be a forum for the presentation of mathematical ideas or ideas about Mathematics. The Colloquium welcomes the participation of faculty, researchers and undergraduate or graduate students, of IST or other institutions, and is seen as an opportunity of bringing together and fostering the building up of ideas in an informal atmosphere.

Organizers: Conceição Amado, Lina Oliveira e Maria João Borges.