Solutions of the Divergence and Related Inequalities

DATES: October 24, 25, 26 and 28, 2016 (4 sessions)
TIME: 16:00 -17:30 h (a total of 6 hours)

We consider the problem of solutions of div u=f vanishing at the boundary of the given domain and with an appropriate Sobolev norm controlled by f. This result is basic in the analysis of the classic equations of mechanics, in particular it is equivalent to the well posedness of the Stokes equations modeling the motion of a viscous incompressible fluid.

First we review several equivalent forms of this basic result and give some historical references. Then we present the constructive approach to obtain solutions of the divergence and show how the norm of these solutions can be proved using the Calderon-Zygmund singular integral operators. We analyze the relation with other results, in particular Korn type and improved Poincare inequalities. Finally we give generalizations to weighted Sobolev norms and some applications to singular domains.

*Registration is free, but inscription is required before 20th October: So as to inscribe send an e-mail to roldan@bcamath.org. Student grants are available. Please, let us know if you need support for travel and accommodation expenses.

• Bcam-Course 2016-10-24-25-26-28