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The mathematical theory of variational inequalities was initially developed to deal with equilibrium problems, precisely the Signorini problem: in that model problem, the functional involved was obtained as the first variation of the involved potential energy.
The obstacle problem is a classic motivating example in the mathematical study of variational inequalities and free boundary problems. The problem is to find the equilibrium position of an elastic membrane whose boundary is held fixed, and which is constrained to lie above a given obstacle.
The birth of the theory of variational inequalities remembered thirty years later (English translation of the contribution title) is an historical paper describing the beginning of the theory of variational inequalities from the point of view of its founder.
Human development theory is a theory which uses ideas from different origins, such as ecology, sustainable development, feminism and welfare economics. It wants to avoid normative politics and is focused on how social capital and instructional capital can be deployed to optimize the overall value of human capital in an economy.
In mathematics, a differential variational inequality (DVI) is a dynamical system that incorporates ordinary differential equations and variational inequalities or complementarity problems. DVIs are useful for representing models involving both dynamics and inequality constraints.
Filippov's theory only allows for discontinuities in the derivative (), but allows no discontinuities in the state, i.e. () need be continuous. Schatzman and later Moreau (who gave it the currently accepted name) extended the notion to measure differential inclusion (MDI) in which the inclusion is evaluated by taking the limit from above for x ...
Variational methods in general relativity, a family of techniques using calculus of variations to solve problems in Einstein's general theory of relativity; Finite element method is a variational method for finding numerical solutions to boundary-value problems in differential equations;
The theory of Michael Commons' model of hierarchical complexity is also relevant. The description of stages in these theories is more elaborate and focuses on underlying mechanisms of information processing rather than on reasoning as such. In fact, development in information processing capacity is invoked to explain the development of reasoning.