Homeomorphic Sobolev Extensions of Parametrizations of Jordan Curves
Explore homeomorphic Sobolev extensions of Jordan curve parametrizations, examining conditions for finite energy deformations and recent findings in this mathematical field.
Elliptic Regularity and Singularity
Explore elliptic regularity and singularity in mathematics with Federico Franceschini's concise talk, gaining insights into advanced mathematical concepts and their applications.
Sobolev Spaces: The Case N = 1 - Part 3
Explore advanced concepts in Sobolev spaces, focusing on the case N = 1, with Prof. S Kesavan from the Institute of Mathematical Sciences.
Sobolev Spaces: Density of Test Functions in Euclidean Space - Part 2
Explore density of test functions in Sobolev spaces on Euclidean space, advancing understanding of mathematical analysis.
Sobolev Spaces: Definition, Notations, and Completeness - Part 1
Explore Sobolev spaces: definition, notations, and completeness. Gain foundational knowledge in this essential mathematical concept for advanced analysis.
Weak Solutions of Elliptic Boundary Value Problems - Part 1
Explore weak solutions for elliptic boundary value problems, focusing on the Dirichlet problem for the Laplacian. Gain insights into advanced mathematical concepts and problem-solving techniques.
Function Spaces on Quantum Tori and Their Applications
Explore Sobolev, Besov, and Triebel-Lizorkin spaces on quantum tori, examining their properties and applications in pseudo-differential theory and noncommutative geometry.
The Computational Theory of Riemann-Hilbert Problems - Lecture 4
Explores computational approaches to Riemann-Hilbert problems, covering Cauchy integrals, Sobolev spaces, and applications to nonlinear equations like Schrödinger and KdV, with code demonstrations and numerical solution techniques.
Flows of Irregular Vector Fields in Fluid Dynamics - Lecture 6
Explore modern techniques for analyzing flows of irregular vector fields, with applications to fluid dynamics and turbulence theory. Gain insights into nonlinear PDEs and Euler/Navier-Stokes equations.
Flows of Irregular Vector Fields in Fluid Dynamics - Lecture 5
Explore modern techniques for analyzing flows of irregular vector fields, including quantitative regularity estimates, nonuniqueness solutions, and applications to fluid dynamics PDEs.
Flows of Irregular Vector Fields in Fluid Dynamics - Lecture 4
Explore modern techniques for analyzing flows of irregular vector fields, including quantitative regularity estimates, nonuniqueness solutions, and applications to fluid dynamics PDEs.
Flows of Irregular Vector Fields in Fluid Dynamics - Lecture 3
Explore modern techniques for analyzing flows of irregular vector fields, including quantitative regularity estimates, nonuniqueness solutions, and applications to fluid dynamics PDEs.
Flows of Irregular Vector Fields in Fluid Dynamics - Lecture 2
Explore modern techniques for analyzing flows of irregular vector fields, including quantitative regularity estimates, nonuniqueness solutions, and applications to fluid dynamics PDEs.
Flows of Irregular Vector Fields in Fluid Dynamics - Lecture 1
Explore modern concepts in flows of irregular vector fields, including quantitative regularity estimates, nonuniqueness solutions, and applications to fluid dynamics and turbulence theory.
Minimization Problems for the Axisymmetric Neo-Hookean Energy
Explore minimization problems for axisymmetric neo-Hookean energy, focusing on existence of minimizers, energy concentration, and bounds for relaxed energy in critical Sobolev cases.
Weakly Turbulent Solution to the Schrödinger Equation on the 2D Torus with Potential
Explore a smooth solution to the linear Schrödinger equation on a 2D torus, examining logarithmic H^1 Sobolev norm growth and infinite-time blowup using adapted CKSTT techniques.
Advection-Diffusion Problems on Polygonal Meshes
Explore advanced mathematical techniques for solving advection-diffusion PDEs on polygonal meshes, covering high-order finite elements, WENO methods, and practical applications in geosciences.