Calculus of variations | Partial differential equations

Hilbert's nineteenth problem

Hilbert's nineteenth problem is one of the 23 Hilbert problems, set out in a list compiled in 1900 by David Hilbert. It asks whether the solutions of regular problems in the calculus of variations are always analytic. Informally, and perhaps less directly, since Hilbert's concept of a "regular variational problem" identifies precisely a variational problem whose Euler–Lagrange equation is an elliptic partial differential equation with analytic coefficients, Hilbert's nineteenth problem, despite its seemingly technical statement, simply asks whether, in this class of partial differential equations, any solution function inherits the relatively simple and well understood structure from the solved equation. Hilbert's nineteenth problem was solved independently in the late 1950s by Ennio De Giorgi and John Forbes Nash, Jr. (Wikipedia).

Video thumbnail

C74 Example problem

A first example problem solving a linear, second-order, homogeneous, ODE with variable coefficients around a regular singular point.

From playlist Differential Equations

Video thumbnail

C49 Example problem solving a system of linear DEs Part 1

Solving an example problem of a system of linear differential equations, where one of the equations is not homogeneous. It's a long problem, so this is only part 1.

From playlist Differential Equations

Video thumbnail

C56 Continuation of previous problem

Adding a bit more depth to the previous problem.

From playlist Differential Equations

Video thumbnail

C76 A first example problem calculating the Laplace transform

Calculating our first Laplace transform.

From playlist Differential Equations

Video thumbnail

B25 Example problem solving for a Bernoulli equation

See how to solve a Bernoulli equation.

From playlist Differential Equations

Video thumbnail

B01 An introduction to separable variables

In this first lecture I explain the concept of using the separation of variables to solve a differential equation.

From playlist Differential Equations

Video thumbnail

C73 Introducing the theorem of Frobenius

The theorem of Frobenius allows us to calculate a solution around a regular singular point.

From playlist Differential Equations

Video thumbnail

Problem Set 9

Sample exam questions on periodic functions, odd and even extensions, and Fourier series.

From playlist MATH2018 Engineering Mathematics 2D

Video thumbnail

IMS Public Lecture: Foundations of Mathematics: An Optimistic Message

Stephen G. Simpson, Pennsylvania State University, USA

From playlist Public Lectures

Video thumbnail

An introduction to Invariant Theory - Harm Derksen

Optimization, Complexity and Invariant Theory Topic: An introduction to Invariant Theory Speaker: Harm Derksen Affiliation: University of Michigan Date: June 4, 2018 For more videos, please visit http://video.ias.edu

From playlist Mathematics

Video thumbnail

What Every Physicist Should Know About String Theory: Edward Witten

https://strings2015.icts.res.in/talkTitles.php Table of Contents (powered by https://videoken.com) 0:00:00 Introduction 0:01:05 [Talk: What Every Physicist Should Know About String Theory by Edward Witten] 0:02:46 Anyone who has studied physics is familiar with the fact that while physics

From playlist Strings 2015 conference

Video thumbnail

Hilbert Space Techniques in Complex Analysis and Geometry (Lecture 9) by Dror Varolin

PROGRAM CAUCHY-RIEMANN EQUATIONS IN HIGHER DIMENSIONS ORGANIZERS: Sivaguru, Diganta Borah and Debraj Chakrabarti DATE: 15 July 2019 to 02 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Complex analysis is one of the central areas of modern mathematics, and deals with holomo

From playlist Cauchy-Riemann Equations in Higher Dimensions 2019

Video thumbnail

"New Paradigms in Invariant Theory" - Roger Howe, Yale University [2011]

HKUST Institute for Advanced Study Distinguished Lecture New Paradigms in Invariant Theory Speaker: Prof Roger Howe, Yale University Date: 13/6/2011 Video taken from: http://video.ust.hk/Watch.aspx?Video=6A41D5F6B1A790DC

From playlist Mathematics

Video thumbnail

Background material on the Cauchy-Riemann equations (Lecture 1) by Debraj Chakrabarti

PROGRAM CAUCHY-RIEMANN EQUATIONS IN HIGHER DIMENSIONS ORGANIZERS: Sivaguru, Diganta Borah and Debraj Chakrabarti DATE: 15 July 2019 to 02 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Complex analysis is one of the central areas of modern mathematics, and deals with holomo

From playlist Cauchy-Riemann Equations in Higher Dimensions 2019

Video thumbnail

Hilbert Space Techniques in Complex Analysis and Geometry (Lecture 5) by Dror Varolin

PROGRAM CAUCHY-RIEMANN EQUATIONS IN HIGHER DIMENSIONS ORGANIZERS: Sivaguru, Diganta Borah and Debraj Chakrabarti DATE: 15 July 2019 to 02 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Complex analysis is one of the central areas of modern mathematics, and deals with holomo

From playlist Cauchy-Riemann Equations in Higher Dimensions 2019

Video thumbnail

Hilbert Space Techniques in Complex Analysis and Geometry (Lecture 10) by Dror Varolin

PROGRAM CAUCHY-RIEMANN EQUATIONS IN HIGHER DIMENSIONS ORGANIZERS: Sivaguru, Diganta Borah and Debraj Chakrabarti DATE: 15 July 2019 to 02 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Complex analysis is one of the central areas of modern mathematics, and deals with holomo

From playlist Cauchy-Riemann Equations in Higher Dimensions 2019

Video thumbnail

The Geometry of Hilbert's 13th problem - Jesse Wolfson

Special Seminar on Hilbert's 13th Problem I Topic: The Geometry of Hilbert's 13th problem Speaker: Jesse Wolfson Affiliation: University of California, Irvine Date: December 5, 2019 For more video please visit http://video.ias.edu

From playlist Mathematics

Video thumbnail

Hilbert Space Techniques in Complex Analysis and Geometry (Lecture 11) by Dror Varolin

PROGRAM CAUCHY-RIEMANN EQUATIONS IN HIGHER DIMENSIONS ORGANIZERS: Sivaguru, Diganta Borah and Debraj Chakrabarti DATE: 15 July 2019 to 02 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Complex analysis is one of the central areas of modern mathematics, and deals with holomo

From playlist Cauchy-Riemann Equations in Higher Dimensions 2019

Video thumbnail

Differential Equation - 2nd Order (30 of 54) Initial Value Problem

Visit http://ilectureonline.com for more math and science lectures! In this video I will find y(t)=?, given y”-y'-2y=0, y(0)=2, and y'(0)=7. Next video in this series can be seen at: https://youtu.be/1-mhqyPmoGM

From playlist DIFFERENTIAL EQUATIONS 11 - 2nd ORDER, A COMPLETE OVERVIEW

Related pages

Functional (mathematics) | Elliptic partial differential equation | Analytic function | David Hilbert | Laplace's equation | Liouville's equation | Calculus of variations | Lipschitz continuity | Euler–Lagrange equation | Gradient | Partial differential equation | Émile Picard | A priori estimate | Counterexample | Potential theory