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MARC 21

Linear and Quasilinear Parabolic Problems: Volume II: Function Spaces
Tag	Description
020	$a9783030117634
082	$a515.7
099	$aOnline Resource: Birkhäuser
100	$aAmann, Herbert.$d1938-$eauthor.
245	$aLinear and Quasilinear Parabolic Problems$h[EBook]$bVolume II: Function Spaces$cby Herbert Amann.
250	$a1st ed. 2019.
260	$aCham$bSpringer International Publishing$c2019.
300	$aXVI, 462 pages$bonline resource.
440	$aMonographs in Mathematics,$v106
505	$aRestriction-Extension Pairs -- Sequence Spaces -- Anisotropy -- Classical Spaces -- Besov Spaces -- Intrinsic Norms, Slobodeckii and Hölder Spaces -- Bessel Potential Spaces -- Triebel-Lizorkin Spaces -- Point-Wise Multiplications -- Compactness -- Parameter-Dependent Spaces.
520	$aThis 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.
538	$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
710	$aSpringerLink (Online service)
830	$aMonographs in Mathematics,$v106
856	$uhttps://doi.org/10.1007/978-3-030-11763-4