On Density of Sobolev Functions on Euclidean Domains
Explore recent findings on Sobolev space density, removability of measure zero sets, and extension operators in Euclidean domains. Gain insights into advanced mathematical concepts and their applications.
Borderline Sobolev Inequalities on Symmetric Spaces with Applications
Explores Bourgain-Brezis estimate for symmetric spaces, applying it to wave, Schrodinger, Maxwell equations and 2D Navier-Stokes flow. Presents joint research on advanced mathematical concepts in functional analysis.
Edgard Pimentel - Regularity Theory for Nonlinear PDEs
Explore recent developments in regularity theory for nonlinear PDEs, covering compactness, stability, and scaling arguments. Learn about fully nonlinear PDEs, Isaacs equation, and free boundary problems.
Henrik Shahgholian - Free Boundaries on Lattice, and Their Scaling Limits
Explore lattice-based potential theory, examining harmonic functions and free boundary problems. Discover intriguing numerical results and their implications for facet formation in scaling limits.
NOC - Partial Differential Equations for Engineers - Solution
Explore advanced techniques for solving partial differential equations in engineering, covering various coordinate systems and problem types across multiple dimensions.
Mathematics III
Explore advanced mathematical concepts including ODEs, improper integrals, series solutions, Bessel functions, Laplace transformations, and partial differential equations.
Comprehensive Fluids, Entropy Hierarchies, and Flocking - SIAM PDE Seminar
Exploring compressible fluid equations, entropy hierarchies, and flocking dynamics. Covers Navier-Stokes models, nonlocal collective dynamics, and mathematical proofs for fluid behavior and emergent organization.
Shock Formation and Vorticity Creation for Compressible Euler
Exploration of shock formation and vorticity creation in compressible Euler equations, featuring constructive proofs, self-similar variables, and analysis of singularities in multiple dimensions.
Analysis Seminar - Up to the Boundary Gradient Estimates in Bernoulli Type Free Boundary Problems
Explore recent advances in gradient estimates for viscosity solutions of free boundary problems, featuring new Inhomogeneous Pucci Barriers and innovative proof techniques inspired by Harmonic Analysis.
Introduction to Theory and Numerics of Partial Differential Equations - Lecture 5
Explore numerical methods for solving partial differential equations, focusing on techniques essential for gravitational wave astronomy and computational relativity.
Introduction to Theory and Numerics of Partial Differential Equations - Lecture 2
Explore numerical methods for solving partial differential equations, focusing on techniques essential for gravitational wave astronomy and computational relativity.
Introduction to Theory and Numerics of Partial Differential Equations - Lecture 3
Explore numerical methods for solving partial differential equations, focusing on techniques essential for gravitational wave astronomy and computational relativity.
Introduction to Theory and Numerics of Partial Differential Equations - Lecture 1
Explore fundamental concepts and numerical techniques for solving partial differential equations, essential for modeling complex physical phenomena in gravitational-wave astronomy and astrophysics.
Boundary Problems for Incompressible Fluids by Senjo Shimizu
Exploration of free boundary problems in incompressible fluid dynamics, discussing mathematical approaches and recent developments in this complex area of fluid mechanics.
Complex Analysis - Analytic Functions Solve Laplace's Equation
Explore how analytic complex functions' real and imaginary parts solve Laplace's equation, introducing harmonic functions in this in-depth mathematical analysis.
Deriving the Heat Equation in 2D and 3D and in N Dimensions with Control Volumes and Vector Calculus
Explore the derivation of the heat equation in multiple dimensions using Gauss's theorem, control volumes, and vector calculus techniques for a comprehensive understanding of heat transfer.
Partial Differential Equations Overview
Explore the mathematical language of physical phenomena with an overview of partial differential equations, covering canonical PDEs, linear superposition, and nonlinear PDEs like Burgers Equation.
Laplace Transform Solutions to PDEs
Explore Laplace transform techniques for solving partial differential equations, enhancing your understanding of advanced mathematical methods in engineering applications.
Numerical Solution to Laplace's Equation in Matlab - Intro to Fourier Series
Explore numerical solutions to Laplace's Equation using MATLAB and get introduced to Fourier Series in this engineering mathematics lecture, with practical code examples and comprehensive notes provided.
Heat Equation in 2D and 3D - 2D Laplace Equation on Rectangle
Explore multidimensional heat equations and the 2D Laplace equation on rectangles, advancing your understanding of engineering mathematics and partial differential equations.
Analytic Solution to Laplace's Equation in 2D - On Rectangle
Explore the analytic solution to Laplace's equation in 2D on a rectangle, enhancing your understanding of engineering mathematics and partial differential equations.