Beyond Sobolev and Besov

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The book explores the intricate relationship between sophisticated function spaces and the regularity of solutions to partial differential equations (PDEs), linking these concepts to their numerical solutions. It is divided into three parts: an introduction to function spaces, an in-depth examination of regularity in Besov and fractional Sobolev spaces for various types of PDEs, and a discussion on traces in multiple function spaces. The work emphasizes adaptive numerical schemes and provides insights into both linear and nonlinear equations, with a particular focus on parabolic PDEs.