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4:00 pm Monday, December 3, 2012 Geometry-Analysis Seminar: New Inequalities and Spaces of Sobolev Typeby Giles Auchmuty (University of Houston) in HB453- Abstract: This talk will describe recent well-posedness results for Poisson's equation on R^N with N being at least 3. Instead of seeking solutions of the equation in standard Sobolev spaces, the problem is posed on spaces where an integrability condition is replaced by a condition of decay at innity. These spaces will be Banach or Hilbert spaces under natural norms and inner products. Some sharp imbedding theorems will be described that are related to boundedness and intrinsic decay rates at infinity for solutions of Poisson's equation both on R^N and on exterior regions. When N = 3, these provide new results and estimates for classical gravitational and electrostatic fields.
Submitted by hardt@rice.edu |