Regularity Results for Degenerate Phase Transitions

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Masterclass in Applied Nonlinear PDEs


This talk derives a quantitative modulus of continuity, up to the parabolic boundary, for solutions of the Cauchy–Dirichlet problem associated with a phase transition modeled upon the p-degenerate two-phase Stefan problem. Even in the classical case p = 2, this represents a twofold improvement concerning the state-of-the-art, in the sense that we discard one logarithm iteration and obtain an explicit value for the exponent appearing in the modulus.

Brief Biography

Miguel Urbano is a Professor of Applied Mathematics and Computational Sciences at the King Abdullah University of Science and Technology (KAUST) in Saudi Arabia. Before joining KAUST in 2022, he had been a Full Professor at the University of Coimbra since 2009.  He is an expert on free boundary problems and regularity theory for nonlinear PDEs, particularly on the method of intrinsic scaling for singular or degenerate-type equations. He is a Corresponding Member of the Lisbon Academy of Sciences and Editor-in-Chief of Portugaliae Mathematica.

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