Non Homogeneous Boundary Value Problems And Applications By J L Lions And E Magenes
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Non Homogeneous Boundary Value Problems And Applications By J L Lions And E Magenes
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Author : Jacques Louis Lions
language : en
Publisher:
Release Date : 1972
Non Homogeneous Boundary Value Problems And Applications By J L Lions And E Magenes written by Jacques Louis Lions and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Boundary value problems categories.
Non Homogeneous Boundary Value Problems And Applications
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Author : Jacques Louis Lions
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Non Homogeneous Boundary Value Problems And Applications written by Jacques Louis Lions and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Non Homogeneous Boundary Value Problems And Applications
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Author : Jacques Louis Lions
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Non Homogeneous Boundary Value Problems And Applications written by Jacques Louis Lions and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
1. Our essential objective is the study of the linear, non-homogeneous problems: (1) Pu = I in CD, an open set in RN, (2) fQjtl = gj on am (boundary of m), lor on a subset of the boundm"J am 1
Non Homogeneous Boundary Value Problems And Applications
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Author : J. L. Lions
language : de
Publisher:
Release Date : 1972
Non Homogeneous Boundary Value Problems And Applications written by J. L. Lions and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with categories.
Non Homogeneous Boundary Value Problems And Applications
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Author : Jacques Louis Lions
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Non Homogeneous Boundary Value Problems And Applications written by Jacques Louis Lions and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
I. In this second volume, we continue at first the study of non homogeneous boundary value problems for particular classes of evolu tion equations. 1 In Chapter 4 , we study parabolic operators by the method of Agranovitch-Vishik [lJ; this is step (i) (Introduction to Volume I, Section 4), i.e. the study of regularity. The next steps: (ii) transposition, (iii) interpolation, are similar in principle to those of Chapter 2, but involve rather considerable additional technical difficulties. In Chapter 5, we study hyperbolic operators or operators well defined in thesense of Petrowski or Schroedinger. Our regularity results (step (i)) seem to be new. Steps (ii) and (iii) are all3.logous to those of the parabolic case, except for certain technical differences. In Chapter 6, the results of Chapter'> 4 and 5 are applied to the study of optimal control problems for systems governed by evolution equations, when the control appears in the boundary conditions (so that non-homogeneous boundary value problems are the basic tool of this theory). Another type of application, to the characterization of "all" well-posed problems for the operators in question, is given in the Ap pendix. Still other applications, for example to numerical analysis, will be given in Volume 3.
Non Homogeneous Boundary Value Problems And Applications
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Author : Jacques-Louis Lions
language : en
Publisher:
Release Date :
Non Homogeneous Boundary Value Problems And Applications written by Jacques-Louis Lions and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with Boundary value problems categories.
Non Homogeneous Boundary Value Problems And Applications
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Author : Jacques Louis Lions
language : en
Publisher: Springer
Release Date : 2011-11-15
Non Homogeneous Boundary Value Problems And Applications written by Jacques Louis Lions and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-15 with Mathematics categories.
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.
Non Homogeneous Boundary Value Problems And Applications
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Author : Jacques-Louis Lions
language : en
Publisher:
Release Date : 1972
Non Homogeneous Boundary Value Problems And Applications written by Jacques-Louis Lions and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Boundary value problems categories.
Non Homogeneous Boundary Value Problems And Applications Die Grund Der Math Wiss In Einzel 183
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Author : Jacques-Louis Lions
language : en
Publisher:
Release Date : 1972
Non Homogeneous Boundary Value Problems And Applications Die Grund Der Math Wiss In Einzel 183 written by Jacques-Louis Lions and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Boundary value problems categories.
Non Homogeneous Boundary Value Problems And Applications Vol 1 3
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Author : J. L. Lions
language : en
Publisher:
Release Date : 1972
Non Homogeneous Boundary Value Problems And Applications Vol 1 3 written by J. L. Lions and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Boundary value problems categories.