Free Boundary Problems and Regularity Theory
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Free Boundary Problems and Regularity Theory

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Free boundary problems are a category of mathematical problems characterised by the determination of both the solution to a partial differential equation and the dynamic boundary where the solution is defined. These problems are prevalent in various scientific and engineering contexts, including fluid dynamics, materials science and biological growth processes, where the boundary conditions are not predetermined but instead form part of the solution itself. Regularity theory examines the smoothness and structural properties of the solutions and their boundaries. Regularity results are essentia...