Ruirui Wu, University of Washingotn
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PDL C-401
We prove a uniqueness result for the Calderón problem for the quasilinear conductivity equation on a bounded domain in R^n. The proof of the result is based on the higher order linearization method. In contrast to the higher dimensional case, the proof involves delicate analysis of the correction terms of Bukhgeim type complex geometric solutions (CGOs), which have only limited decay. To prove our results, we construct suitable families of CGOs whose phase functions have and do not have critical points. We also combine stationary phase analysis with estimates for the correction terms of the CGOs. This is a joint work with Tony Liimatainen at University of Helsinki.