Regularity of Degenerate Partial Differential Equations and Applications

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Partial Differential Equations (PDEs) is the mathematical language science uses to model a wide variety of processes like heat flow, wave propagation, biological functions in humans and animals, financial markets, celestial dynamics, and the engineering of structures, among many other processes. Most scientific principles and theories can be elegantly stated using differential equations. For this reason PDEs have been extensively studied ever since Newton and Leibniz set the foundations for differential Calculus, and today there is a good understanding of what is now called classical theory of PDEs. However, many applications do not conform to the restrictions of classical models, as the equations governing their nature are ''degenerate'' in some aspects.