Premium
Linear functionals on nonlinear spaces and applications to problems from viscoplasticity theory
Author(s) -
Pompe Waldemar
Publication year - 2007
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.943
Subject(s) - mathematics , surjective function , banach space , monotone polygon , reflexive space , pseudo monotone operator , space (punctuation) , pure mathematics , nonlinear system , regular polygon , viscoplasticity , approximation property , dual space , mathematical analysis , operator space , finite rank operator , interpolation space , functional analysis , geometry , finite element method , biochemistry , chemistry , physics , quantum mechanics , constitutive equation , thermodynamics , linguistics , philosophy , gene
A classical result in the theory of monotone operators states that if C is a reflexive Banach space, and an operator A : C → C * is monotone, semicontinuous and coercive, then A is surjective. In this paper, we define the ‘dual space’ C * of a convex, usually not linear, subset C of some Banach space X (in general, we will have C * ⊃ X * ) and prove an analogous result. Then, we give an application to problems from viscoplasticity theory, where the natural space to look for solutions is not linear. Copyright © 2007 John Wiley & Sons, Ltd.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom