Abstract
SHS investigation development is considered from the geographical and historical viewpoint. 3 stages are described. Within Stage 1 the work was carried out in the Department of the Institute of Chemical Physics in Chernogolovka where the scientific discovery had been made. At Stage 2 the interest to SHS arose in different cities and towns of the former USSR. Within Stage 3 SHS entered the international scene. Now SHS processes and products are being studied in more than 50 countries.
Abstract
Sobolev spaces were defined by the Russian mathematician Sergei Lvovich Sobolev (1908-1989) in the 1930s. Denoted by Wm;p (Ω) ; Sobolev spaces are the space of functions whose all m-th order generalized derivatives are in Lp (Ω) space and partial derivatives of these spaces satisfy certain integrability conditions. Notice that generalized derivative refers to the weak derivative which is defined in the previous chapter. In this part we present fundamental properties of Sobolev spaces with several examples. For further reading on Sobolev spaces we cite [29–32].
Keywords:
Sobolev space, Banach space, dual space, Sobolev space of real order, Sobolev space of negative order, weighted Lebesgue space, Schwartz space, Plancherel theorem, embedding, weight function.
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Authors:Bentham Science Books