Calculus of variations

Quasiconvexity (calculus of variations)

In the calculus of variations, a subfield of mathematics, quasiconvexity is a generalisation of the notion of convexity. It is used to characterise the integrand of a functional and related to the existence of minimisers. Under some natural conditions, quasiconvexity of the integrand is a necessary and sufficient condition for a functional to be lower semi-continuous in the weak topology, for a sufficient regular domain . By compactness arguments (Banach–Alaoglu theorem) the existence of minimisers of weakly lower semicontinuous functionals may then follow from the direct method.This concept was introduced by Morrey in 1952. This generalisation should not be confused with the same concept of a quasiconvex function which has the same name. (Wikipedia).

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Find a Particular Solution to a Nonhomgeneous DE Using Variation of Parameters

This video explains how to determine a particular solution to a linear second order differential equation using the method of variation of parameters. http://mathispower4u.com

From playlist Linear Second Order Nonhomogeneous Differential Equations: Variation of Parameters

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Multivariable Calculus | Definition of partial derivatives.

We give the definition of the partial derivative of a function of more than one variable. In addition, we present some examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Multivariable Calculus

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Derive the Variation of Parameters Formula to Solve Linear Second Order Nonhomogeneous DEs

This video derives or proves the variation of parameters formula used to find a particular solution and solve linear second order nonhomogeneous differential equations. Site: http://mathispower4u.com

From playlist Linear Second Order Nonhomogeneous Differential Equations: Variation of Parameters

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Pre-Calculus - Types of variation

In this video I'll introduce the basic types of variation like direct, inverse, and joint variation. Near the end I'll also talk about combined variation where we put these basic forms together. Remember to see how the variable are connected for a clue on the type of variation. For more

From playlist Pre-Calculus

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Leonid Potyagailo - Similar Relatively hyperbolic actions of a group

Leonid Potyagailo (Université de Lille 1, France) This is a joint work with Victor Gerasimov (University of Belo Horisonte, Brasil). Let a discrete group $G$ possess two convergence actions by homeomorphisms on compacta $X$ and $Y$. Consider the following question: does there exist a con

From playlist T1-2014 : Random walks and asymptopic geometry of groups.

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Proof that every Differentiable Function is Continuous

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys A proof that every differentiable function is continuous.

From playlist Calculus

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Algebraic Ending Laminations and Quasiconvexity by Mahan Mj

Surface Group Representations and Geometric Structures DATE: 27 November 2017 to 30 November 2017 VENUE:Ramanujan Lecture Hall, ICTS Bangalore The focus of this discussion meeting will be geometric aspects of the representation spaces of surface groups into semi-simple Lie groups. Classi

From playlist Surface Group Representations and Geometric Structures

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A New Cubulation Theorem for Hyperbolic Groups- Daniel Groves

Daniel Groves University of Illinois, Chicago October 27, 2015 https://www.math.ias.edu/seminars/abstract?event=83384 We prove that if a hyperbolic group G acts cocompactly on a CAT(0) cube complexes and the cell stabilizers are quasiconvex and virtually special, then G is virtually spec

From playlist Geometric Structures on 3-manifolds

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Partial Implicit Differentiation

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From playlist Functions of Several Variables - Calculus

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Introduction to Direct Variation, Inverse Variation, and Joint Variation

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Introduction to Direct Variation, Inverse Variation, and Joint Variation

From playlist 3.7 Modeling Using Variation

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Irène Waldspurger: Rank optimality for the Burer-Monteiro factorization

The Burer-Monteiro factorization is a classical heuristic used to speed up the solving of large scale semidefinite programs when the solution is expected to be low rank: One writes the solution as the product of thinner matrices, and optimizes over the (low-dimensional) factors instead of

From playlist Control Theory and Optimization

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Continuity vs Partial Derivatives vs Differentiability | My Favorite Multivariable Function

In single variable calculus, a differentiable function is necessarily continuous (and thus conversely a discontinuous function is not differentiable). In multivariable calculus, you might expect a similar relationship with partial derivatives and continuity, but it turns out this is not th

From playlist Calculus III: Multivariable Calculus (Vectors, Curves, Partial Derivatives, Multiple Integrals, Optimization, etc) **Full Course **

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Calculus of Variations ft. Flammable Maths

Flammable Maths: https://www.youtube.com/channel/UCtAIs1VCQrymlAnw3mGonhw Leibnitz Rule: https://www.youtube.com/watch?v=wkh1Y7R1sOw This video is an introduction to the calculus of variations. We go over what variational calculus is trying to solve, and derive the Euler-Lagrange equatio

From playlist Analysis

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The Palais-Smale Theorem and the Solution of Hilbert’s 23 Problem - Karen Uhlenbeck

Members' Seminar Topic: The Palais-Smale Theorem and the Solution of Hilbert’s 23 Problem Speaker: Karen Uhlenbeck Affiliation: The University of Texas at Austin; Distinguished Visiting Professor, School of Mathematics Date: April 6, 2020 For more video please visit http://video.ias.edu

From playlist Mathematics

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Lec 23 | MIT 18.086 Mathematical Methods for Engineers II

Calculus of Variations / Weak Form View the complete course at: http://ocw.mit.edu/18-086S06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 18.086 Mathematical Methods for Engineers II, Spring '06

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Soviet Era Math Book for Beginners and Mathematical Experts

This book states that it is written with beginners in mind but it can also be of use to expert mathematicians. The first half of the book is on Differential Equations and the second half is on the Calculus of Variations. In this video I will show you this book and I will also solve a diffe

From playlist Book Reviews

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A Taste of Calculus of Variations

Dirichlet's Principle In this video, I give you a taste of calculus of variations by illustrating Dirichlet's principle, which says that a function u is a minimizer of a certain Dirichlet energy (kinetic + potential energy) if and only if u solves Poisson's equation. This is a neat way of

From playlist Partial Differential Equations

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2_1 Sequences

Convergence and sequences.

From playlist Advanced Calculus / Multivariable Calculus

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Karen Uhlenbeck: Some Thoughts on the Calculus of Variations

Abstract: I will talk about some of the classic problems in the calculus of variations, and describe some of the mathematics which was developed to solve them. We will begin with the Greeks and end with some of the tantalizing problems of today. This lecture was given by the 2019 Abel Lau

From playlist Karen K. Uhlenbeck

Related pages

Carathéodory function | Weak topology | Radon measure | Banach–Alaoglu theorem | Quasiconvex function | Direct method in the calculus of variations | Lipschitz domain | Calculus of variations | Semi-continuity | Sobolev space | Jensen's inequality