Harmonic functions | Partial differential equations | Lemmas in analysis
In mathematics, Weyl's lemma, named after Hermann Weyl, states that every weak solution of Laplace's equation is a smooth solution. This contrasts with the wave equation, for example, which has weak solutions that are not smooth solutions. Weyl's lemma is a special case of elliptic or hypoelliptic regularity. (Wikipedia).
Differential Equations | The Laplace Transform of a Derivative
We establish a formula involving the Laplace transform of the derivative of a function. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist The Laplace Transform
Laplace Equation on the Unit Disk
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Partial Differential Equations
Emmanuel Trélat - Analyse spectrale des Laplaciens sous-Riemanniens, mesure de Weyl
Dans une série de travaux avec Yves Colin de Verdière et Luc Hillairet, nous étudions les propriétés spectrales des Laplaciens sous-Riemanniens, qui sont des opérateurs hypoelliptiques. L'objectif principal est d'obtenir des résultats d'ergodicité quantique, ce que nous avons fait en géo
From playlist Journée Sous-Riemannienne 2016
D. Prandri - Weyl law for singular Riemannian manifolds
In this talk we present recent results on the asymptotic growth of eigenvalues of the Laplace-Beltrami operator on singular Riemannian manifolds, where all geometrical invariants appearing in classical spectral asymptotics are unbounded, and the total volume can be infinite. Under suitable
From playlist Journées Sous-Riemanniennes 2018
Emmy Noether Lecture: Conformal geometry on 4-manifolds — Sun-Yung Alice Chang — ICM2018
Conformal geometry on 4-manifolds Sun-Yung Alice Chang Abstract: In this talk, I will report on the study of a class of integral conformal invariants on 4-manifolds and applications to the study of topology and diffeomorphism type of a class of 4-manifolds. The key ingredient is the study
From playlist Special / Prizes Lectures
Differential Equations | Laplace Transform of a Piecewise Function
We find the Laplace transform of a piecewise function using the unit step function. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist The Laplace Transform
Introduction to Laplace Transforms
Introduction to Laplace Transforms A full introduction. The definition is given, remarks are made, and an example of finding the laplace transform of a function with the definition is done.
From playlist Differential Equations
Derivation of Poisson's Formula for of Laplace's Equation on the Unit Disk: Complex Fourier Series!
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Partial Differential Equations
Alice Chang: Conformal Geometry on 4-manifolds
Abstract: In this talk, I will report on the study of integral conformal invariants on 4-manifolds and applications to the study of topology and diffeomorphism type of a class of 4-manifolds. The key ingredient is the study of the integral of 2 of the Schouten tensor which is the part of i
From playlist Abel in... [Lectures]
Differential Equations | A formula for the Laplace Transform of t^n f(t)
We prove the existence of a formula involving the Laplace transform of t^n f(t). http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist The Laplace Transform
Laplace Eigenvalues on the Rectangle: A Complete Derivation
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Partial Differential Equations
Solution of the Laplace Equation on an Annulus
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Partial Differential Equations
Differential Isomorphism and Equivalence of Algebraic Varieties Board at 49:35 Sum_i=1^N 2/(x-phi_i(y,t))^2
From playlist Fall 2017
From playlist Contributed talks One World Symposium 2020
Discrete Laplace Equation | Lecture 62 | Numerical Methods for Engineers
Derivation of the discrete Laplace equation using the central difference approximations for the partial derivatives. Join me on Coursera: https://www.coursera.org/learn/numerical-methods-engineers Lecture notes at http://www.math.ust.hk/~machas/numerical-methods-for-engineers.pdf Subscr
From playlist Numerical Methods for Engineers
Type I, Type II and front singularities - Pierre Raphaël
Hermann Weyl Lectures Topic: Type I, Type II and front singularities Speaker: Pierre Raphaël Affiliation: University of Cambridge Date: October 4, 2021 In the last forty years, the study of singularity formation has mostly concerned model problems and focusing non linearities. In this s
From playlist Hermann Weyl Lectures
Point-counting and diophantine applications - Jonathan Pila
Hermann Weyl Lectures Topic: Point-counting and diophantine applications Speaker: Jonathan Pila Affiliation: University of Oxford Date: October 23, 2018 For more video please visit http://video.ias.edu
From playlist Hermann Weyl Lectures
Tensor Calculus Lecture 7d: The Voss-Weyl Formula
This course will eventually continue on Patreon at http://bit.ly/PavelPatreon Textbook: http://bit.ly/ITCYTNew Errata: http://bit.ly/ITAErrata McConnell's classic: http://bit.ly/MCTensors Table of Contents of http://bit.ly/ITCYTNew Rules of the Game Coordinate Systems and the Role of Te
From playlist Introduction to Tensor Calculus
Blow up for the energy super critical defocusing NLS - Pierre Raphaël
Hermann Weyl Lectures Topic: Blow up for the energy super critical defocusing NLS Speaker: Pierre Raphaël Affiliation: University of Cambridge Date: October 5, 2021 The defocusing Non Linear Schrödinger equation iut=Δu−u|u|p−1 is a classical model of mathematical physics. For energy sub
From playlist Hermann Weyl Lectures
Suppose that a function u equals to its average value on every ball and every sphere, what can we say about u? It turns out that u has to solve Laplace’s equation! Conversely, if u solves Laplace’s equation, then u must satisfy the above mean-value property. In this video, I state and pro
From playlist Partial Differential Equations