SMS scnews item created by Daniel Daners at Fri 9 Apr 2010 1039
Type: Seminar
Distribution: World
Expiry: 19 Apr 2010
Calendar1: 19 Apr 2010 1500-1600
CalLoc1: Carslaw 273

PDE Seminar

Boundary value problems for elliptic systems with L_2 data


Pascal Auscher
Universitť de Paris-Sud
19 April 2010, 3-4pm, Carslaw Room 273


We describe joint work with Andreas Axelsson. We introduce a setup to study solutions of divergence form second order elliptic systems Lu = 0 on the upper-half space with coefficients having little smoothness on the vertical variable (A Carleson measure estimate introduced by Dahlberg: this estimate being zero meaning that the coefficients do not depend on the vertical variable). In this setup, natural trace spaces on the boundary allow to describe limiting behaviour of our weak solutions u and then to formulate and study Dirichlet, Neumann and Dirichlet-regularity problems. We obtain a perturbation result for well-posedness for small Carleson measures. This yield well-posedness results for a class of elliptic systems extending the known results of Dahlberg and Kenig-Pipher for real symmetric equations. Methods no longer use harmonic measure (which is unavailable) but a first order system formalism in the conormal gradient, the solution of the Kato conjecture and new maximal regularity estimates.

Check also the PDE Seminar page. Enquiries to Florica CÓrstea or Daniel Daners.

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