11:00 am Friday, September 6, 2013
Junior Analysis: On Some Limiting Transmission Problems by Dennis Kriventsov in RLM 10.176
In the theory of electrostatics, a natural situation to consider is that of a discontinuous change in permittivity of a medium across an interface (this happens, for example, in the neighborhood of the boundary between two different homogeneous materials). It is a classical fact that in such situations, the electric potential will be continuous across the interface, while the electric field will form a specific and fully describable discontinuity. This is known in PDE literature as a transmission problem. I will consider a limiting version of this problem from the perspective of regularity theory of elliptic equations. Our main goal will be a uniform Holder estimate proven via the method of De Giorgi. Time permitting, I will mention some extensions, including a "nonlocal transmission problem" for which questions of regularity can be approached from this perspective. Submitted by
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