Non-Homogeneous Boundary Value Problems and Applications: Vol. 1: 181 (Grundlehren der mathematischen Wissenschaften, 181) - Image 1

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Springer Non-Homogeneous Boundary Value Problems and Applications: Vol. 1: 181 (Grundlehren der mathematischen Wissenschaften, 181)

Name: Non-Homogeneous Boundary Value Problems and Applications: Vol. 1: 181 (Grundlehren der mathematischen Wissenschaften, 181)
Brand: Springer
Price: 86.11 GBP
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Differential Equations

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Description

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.

Product Specifications

Brand: Springer
Format: paperback
ASIN: 3642651631
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Mathematical Analysis > Differential Equations
Domain: Amazon UK
Release Date: 15 November 2011
Listed Since: 13 July 2012

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Springer Non-Homogeneous Boundary Value Problems and Applications: Vol. 1: 181 (Grundlehren der mathematischen Wissenschaften, 181)

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