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In mathematics, there is in mathematical analysis a class of Sobolev inequalities, relating norms including those of Sobolev spaces.These are used to prove the Sobolev embedding theorem, giving inclusions between certain Sobolev spaces, and the Rellich–Kondrachov theorem showing that under slightly stronger conditions some Sobolev spaces are compactly embedded in others.
The Proceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment is a quarterly peer-reviewed scientific journal covering research on the design, production, and operation of engineering artefacts for the maritime environment. The journal covers subjects including naval architecture, marine ...
In mathematics, and in particular in mathematical analysis, the Gagliardo–Nirenberg interpolation inequality is a result in the theory of Sobolev spaces that relates the -norms of different weak derivatives of a function through an interpolation inequality.
In mathematics, a Sobolev mapping is a mapping between manifolds which has smoothness in some sense. Sobolev mappings appear naturally in manifold-constrained problems in the calculus of variations and partial differential equations , including the theory of harmonic maps .
In mathematics, the Poincaré inequality [1] is a result in the theory of Sobolev spaces, named after the French mathematician Henri Poincaré. The inequality allows one to obtain bounds on a function using bounds on its derivatives and the geometry of its domain of definition.
Gross was one of the initiators of the study of logarithmic Sobolev inequalities, which he discovered in 1967 for his work in constructive quantum field theory and published later in two foundational papers [11] [12] in which he established these inequalities for the Bosonic and Fermionic cases. The inequalities were named by Gross, who ...
In mathematical analysis, Trudinger's theorem or the Trudinger inequality (also sometimes called the Moser–Trudinger inequality) is a result of functional analysis on Sobolev spaces. It is named after Neil Trudinger (and Jürgen Moser). It provides an inequality between a certain Sobolev space norm and an Orlicz space norm of a
The flow in manifolds is extensively encountered in many industrial processes when it is necessary to distribute a large fluid stream into several parallel streams, or to collect them into one discharge stream, such as in fuel cells, heat exchangers, radial flow reactors, hydronics, fire protection, and irrigation. Manifolds can usually be ...