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Description: |
In this talk we show a unified and general criterion for the uniqueness of critical points of a functional in the presence of constraints such as positivity, boundedness, or fixed mass. Our method relies on convexity properties along suitable paths. To illustrate our method we present a unified proof of known results, as well as new theorems for mean-curvature type operators, fractional Laplacians, Hamiltonian systems, Schrödinger equations, and Gross-Pitaevski systems. Essentially, we build paths to uncover the hidden convexity of the associate functionals.
This is based on a joint work with D. Bonheure, J. Foldes, E. Moreira dos Santos and A. Saldaña (arXiv:1607.05638).
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