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Explore advanced mathematical techniques for solving Bernoulli type free boundary problems beyond traditional minimizer approaches in this 46-minute conference lecture. Learn about a novel compactness and regularity theorem that applies to any critical point of the Alt-Caffarelli functional, not just minimizers, utilizing nonlinear frequency formulas and Naber-Valtorta estimates. Discover how to construct min-max type solutions through mountain pass methods, illustrated with practical applications to gravity water waves. Gain insights into cutting-edge research that extends the well-established existence and regularity theory for free boundary problems, presented as part of the Thematic Programme on "Free Boundary Problems" at the Erwin Schrödinger International Institute for Mathematics and Physics.
