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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis
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Non-Homogeneous Boundary Value Problems and Applications - Vol. 1 (Paperback, Softcover reprint of the original 1st ed. 1972)
Loot Price: R3,389
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Non-Homogeneous Boundary Value Problems and Applications - Vol. 1 (Paperback, Softcover reprint of the original 1st ed. 1972)
Series: Grundlehren der mathematischen Wissenschaften, 181
Expected to ship within 10 - 15 working days
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1. We describe, at first in a very formaI manner, our essential
aim. n Let m be an op en subset of R , with boundary am. In m and
on am we introduce, respectively, linear differential operators P
and Qj' 0 ~ i ~ 'V. By "non-homogeneous boundary value problem" we
mean a problem of the following type: let f and gj' 0 ~ i ~ 'v, be
given in function space s F and G , F being a space" on m" and the
G/ s spaces" on am" ; j we seek u in a function space u/t "on m"
satisfying (1) Pu = f in m, (2) Qju = gj on am, 0 ~ i ~ 'v"])). Qj
may be identically zero on part of am, so that the number of
boundary conditions may depend on the part of am considered 2. We
take as "working hypothesis" that, for fEF and gjEG , j the problem
(1), (2) admits a unique solution u E U/t, which depends 3
continuously on the data . But for alllinear probIems, there is a
large number of choiees for the space s u/t and {F; G} (naturally
linke d together). j Generally speaking, our aim is to determine
families of spaces 'ft and {F; G}, associated in a "natural" way
with problem (1), (2) and con j venient for applications, and also
all possible choiees for u/t and {F; G} j in these families.
General
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