PDE Seminars

October 2011

Fernando López García (WPI), "A right inverse of the divergence operator on domains with cusps"
Thursday, 10/20/2011 3:00 PM-4:00 PM
Stratton Hall, 203
ABSTRACT: Abstract: If   Rn is a bounded domain, the existence of solutions u  H 1()n of div u = f
for f  L2() with vanishing mean value, is a basic result in the analysis of the Stokes equations.
It is known that the above mentioned result holds when  is a Lipschitz domain and that it is not
valid for arbitrary H¨older- domains.
In this talk we will prove that if  is a planar simply connected H¨older- domain, there exist
solutions of div u = f in appropriate weighted Sobolev spaces, where the weights are powers of the
distance to the boundary. Moreover, it can be seen that the powers of the distance in the
obtained results are optimal.
In addition, we will state some stronger results for particular H¨older- domains, presenting power
type cusps of integer dimension, where the weights considered are powers of the distance
to the cusp. These results are also optimal in the sense that the power cannot be improved.

For more information, e-mail ma-chair@wpi.edu.

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