TY - BOOK ID - 46280233 TI - Linear and Quasilinear Parabolic Problems : Volume II: Function Spaces PY - 2019 SN - 3030117634 3030117626 PB - Cham : Springer International Publishing : Imprint: Birkhäuser, DB - UniCat KW - Differential equations, Parabolic. KW - Parabolic differential equations KW - Parabolic partial differential equations KW - Differential equations, Partial KW - Functional analysis. KW - Functional Analysis. KW - Functional calculus KW - Calculus of variations KW - Functional equations KW - Integral equations UR - https://www.unicat.be/uniCat?func=search&query=sysid:46280233 AB - This volume discusses an in-depth theory of function spaces in an Euclidean setting, including several new features, not previously covered in the literature. In particular, it develops a unified theory of anisotropic Besov and Bessel potential spaces on Euclidean corners, with infinite-dimensional Banach spaces as targets. It especially highlights the most important subclasses of Besov spaces, namely Slobodeckii and Hölder spaces. In this case, no restrictions are imposed on the target spaces, except for reflexivity assumptions in duality results. In this general setting, the author proves sharp embedding, interpolation, and trace theorems, point-wise multiplier results, as well as Gagliardo-Nirenberg estimates and generalizations of Aubin-Lions compactness theorems. The results presented pave the way for new applications in situations where infinite-dimensional target spaces are relevant – in the realm of stochastic differential equations, for example. ER -