Search results
Results from the WOW.Com Content Network
The first problem involving a variational inequality was the Signorini problem, posed by Antonio Signorini in 1959 and solved by Gaetano Fichera in 1963, according to the references (Antman 1983, pp. 282–284) and (Fichera 1995): the first papers of the theory were (Fichera 1963) and (Fichera 1964a), (Fichera 1964b).
Khalida Inayat Noor is a Pakistani mathematician who was awarded with Pride of Performance award by the President of Pakistan in 2011. [1] Her research topics include mathematical analysis , variational inequalities , and integral operators .
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 calculus of variations began with the work of Isaac Newton, such as with Newton's minimal resistance problem, which he formulated and solved in 1685, and later published in his Principia in 1687, [2] which was the first problem in the field to be formulated and correctly solved, [2] and was also one of the most difficult problems tackled by variational methods prior to the twentieth century.
Many free boundary problems can profitably be viewed as variational inequalities for the sake of analysis. To illustrate this point, we first turn to the minimization of a function F {\displaystyle F} of n {\displaystyle n} real variables over a convex set C {\displaystyle C} ; the minimizer x {\displaystyle x} is characterized by the condition
Total variation distance is half the absolute area between the two curves: Half the shaded area above. In probability theory, the total variation distance is a statistical distance between probability distributions, and is sometimes called the statistical distance, statistical difference or variational distance.
The Gagliardo-Nirenberg inequality generalizes a collection of well-known results in the field of functional analysis. Indeed, given a suitable choice of the seven parameters appearing in the statement of the theorem, one obtains several useful and recurring inequalities in the theory of partial differential equations:
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.