Elliptic partial differential equations

P-Laplacian

In mathematics, the p-Laplacian, or the p-Laplace operator, is a quasilinear elliptic partial differential operator of 2nd order. It is a nonlinear generalization of the Laplace operator, where is allowed to range over . It is written as Where the is defined as In the special case when , this operator reduces to the usual Laplacian. In general solutions of equations involving the p-Laplacian do not have second order derivatives in classical sense, thus solutions to these equations have to be understood as weak solutions. For example, we say that a function u belonging to the Sobolev space is a weak solution of if for every test function we have where denotes the standard scalar product. (Wikipedia).

Video thumbnail

Physics - Advanced E&M: Ch 1 Math Concepts (13 of 55) What is the Laplacian of a Scalar (Field)?

Visit http://ilectureonline.com for more math and science lectures! In this video I will explain, develop the equation, and give examples of the Laplacian of a scalar (field). Next video in this series can be seen at: https://youtu.be/2VXFzhcGT3U

From playlist PHYSICS 67 ADVANCED ELECTRICITY & MAGNETISM

Video thumbnail

C79 Linear properties of the Laplace transform

The linear properties of the Laplace transform.

From playlist Differential Equations

Video thumbnail

Proof of the Convolution Theorem

Proof of the Convolution Theorem, The Laplace Transform of a convolution is the product of the Laplace Transforms, changing order of the double integral, proving the convolution theorem, www.blackpenredpen.com

From playlist Convolution & Laplace Transform (Nagle Sect7.7)

Video thumbnail

C81 More complex Laplace tranformations

Building on the initial set of Laplace transforms to more complex expressions.

From playlist Differential Equations

Video thumbnail

Dong Zhang (7/27/22): Higher order eigenvalues for graph p-Laplacians

Abstract: The spectrum of the graph p-Laplacian is closely related to many properties of the graph itself. In particular, when p=1, the second eigenvalue coincides with the Cheeger constant. The p-Laplacian, for p greater than 1 and less than 2, can be seen as an extrapolation between the

From playlist Applied Geometry for Data Sciences 2022

Video thumbnail

A Laplacian for Nonmanifold Triangle Meshes - SGP 2020

Authors: Nicholas Sharp and Keenan Crane presented at SGP 2020 https://sgp2020.sites.uu.nl https://github.com/nmwsharp/nonmanifold-laplacian Abstract: We describe a discrete Laplacian suitable for any triangle mesh, including those that are nonmanifold or nonorientable (with or without b

From playlist Research

Video thumbnail

The Hypoelliptic Laplacian: An Introduction - Jean-Michel Bismut

Jean-Michel Bismut Universite de Paris-Sud March 26, 2013 For more videos, visit http://video.ias.edu

From playlist Mathematics

Video thumbnail

Math: Partial Differential Eqn. - Ch.1: Introduction (14 of 42) Understanding the Laplacian Operator

Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is a Laplacian operator by simplifying the function to a single dimension where f(x,y,z)=x^3. Next video in this series can be seen at: https://youtu.be/cyvCDc3kX5Y

From playlist PARTIAL DIFFERENTIAL EQNS CH1 INTRODUCTION

Video thumbnail

Pythagorean Theorem

This geometry video tutorial provides a basic introduction into the pythagorean theorem. It explains how to use it to find missing sides and solve for x. In addition, it provides examples of solving word problems using pythagorean theorem for shapes such as right triangles, squares, rhom

From playlist Geometry Video Playlist

Video thumbnail

Juan Luis Vázquez: The theory of nonlinear diffusion with fractional operators

Abstract: In this talk I will report on some of the progress made by the author and collaborators on the topic of nonlinear diffusion equations involving long distance interactions in the form of fractional Laplacian operators. The nonlinearities are of the following types: porous medium,

From playlist Partial Differential Equations

Video thumbnail

T. Richard - Advanced basics of Riemannian geometry 3

We will present some of the tools used by the more advanced lectures. The topics discussed will include : Gromov Hausdorff distance, comparison theorems for sectional and Ricci curvature, the Bochner formula and basics of Ricci flow.

From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics

Video thumbnail

Francesca Da Lio: Analysis of nonlocal conformal invariant variational problems, Lecture III

There has been a lot of interest in recent years for the analysis of free-boundary minimal surfaces. In the first part of the course we will recall some facts of conformal invariant problems in 2D and some aspects of the integrability by compensation theory. In the second part we will show

From playlist Hausdorff School: Trending Tools

Video thumbnail

T. Richard - Advanced basics of Riemannian geometry 3 (version temporaire)

We will present some of the tools used by the more advanced lectures. The topics discussed will include : Gromov Hausdorff distance, comparison theorems for sectional and Ricci curvature, the Bochner formula and basics of Ricci flow.

From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics

Video thumbnail

Ancient solutions to geometric flows II - Panagiota Daskalopoulos

Ancient solutions to geometric flows II - Panagiota Daskalopoulos Women and Mathematics: Uhlenbeck Lecture Course Topic: Ancient solutions to geometric flows II Speaker: Panagiota Daskalopoulos Affiliation: Columbia University Date: May 21, 2019 For more video please visit http://video.

From playlist Mathematics

Video thumbnail

Boundary driven lattice gas with long jumps by Cedric Bernardin

PROGRAM CLASSICAL AND QUANTUM TRANSPORT PROCESSES : CURRENT STATE AND FUTURE DIRECTIONS (ONLINE) ORGANIZERS: Alberto Imparato (University of Aarhus, Denmark), Anupam Kundu (ICTS-TIFR, India), Carlos Mejia-Monasterio (Technical University of Madrid, Spain) and Lamberto Rondoni (Polytechn

From playlist Classical and Quantum Transport Processes : Current State and Future Directions (ONLINE)2022

Video thumbnail

Network Analysis. Lecture 11. Diffusion and random walks on graphs

Random walks on graph. Stationary distribution. Physical diffusion. Diffusion equation. Diffusion in networks. Discrete Laplace operator, Laplace matrix. Solution of the diffusion equation. Normalized Laplacian. Lecture slides: http://www.leonidzhukov.net/hse/2015/networks/lectures/lectu

From playlist Structural Analysis and Visualization of Networks.

Video thumbnail

Jean Michel BISMUT - Fokker-Planck Operators and the Center of the Enveloping Algebra

The heat equation method in index theory gives an explicit local formula for the index of a Dirac operator. Its Lagrangian counterpart involves supersymmetric path integrals. Similar methods can be developed to give a geometric formula for semi simple orbital integrals associated with the

From playlist Integrability, Anomalies and Quantum Field Theory

Video thumbnail

What Is the Laplacian?

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

Video thumbnail

Geometry, Fluids and the Laplacian - Magdalena Czubak

Glimpses of Mathematics, Now and Then: A Celebration of Karen Uhlenbeck's 80th Birthday Topic: Geometry, Fluids and the Laplacian Speaker: Magdalena Czubak Affiliation: University of Colorado Date: September 18, 2022 We are interested in a fluid flow on a general Riemannian manifold.  Th

From playlist Glimpses of Mathematics, Now and Then: A Celebration of Karen Uhlenbeck's 80th Birthday

Related pages

Weak solution | Laplace operator | Mathematics | Elliptic operator | Differentiable function | Sobolev space | Trace operator