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Gradient Estimates for Elliptic Equations and Systems from Composite Material
by
Yanyan Li
Rutgers University
We present some results on gradient estimates for elliptic equations and systems from composite material. The coefficients of the equations and systems are piecewise smooth. Degenerate elliptic equations are allowed. In the elliptic case, the estimates are, even though depending on the size of the surfaces of discountinuity of the coefficients, independent of the distance between these surfaces. The results described in this talk include those in earlier joint works with M. Vogelius (2000), with L. Nirenberg (2003), and recent and ongoing joint works with Ellen ShiTing Bao and Biao Yin which concern degenerate elliptic equations and systems (e.g. the perfect conductivity problem). We will also describe some open problems in this direction.
Date received: September 20, 2007
Copyright © 2007 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cavp-16.