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Trace Inequality for the Fractional Laplacian

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If you have a question about this talk, please contact Edward Mottram.

Trace inequalities, and inequalities in general, play a major role in Analysis. They can help us estimate decay and remainder terms, solve complicated minimization problems and even show greater regularity of a given function. The most interesting of these inequalities are ones that are sharp, i.e. ones that provide the best possible information. In this talk I will discuss a newly discovered sharp inequality connecting between a trace of a function and its fractional Laplacian. We will also find the appropriate geometrical space where the inequality is still valid and classify its minimizers completely. This talk is based on a joint work with Prof. Michael Loss.

This talk is part of the Cambridge Analysts' Knowledge Exchange series.

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