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Recent research activities on sharp constants and optimal inequalities have shown their impact on a deeper understanding of geometric, analytical and other phenomena in the context of partial differential equations and mathematical physics. These intrinsic questions have applications not only to a-priori estimates or spectral theory but also to numerics, economics, optimization, etc.
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Andrea Cianchi, Maria J. Esteban, Bernd Kawohl, Optimal Constants in the Theory of Sobolev Spaces and PDEs. Oberwolfach Rep. 7 (2010), no. 1, pp. 325–371DOI 10.4171/OWR/2010/08