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#Sobolev Spaces

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Hausdorff Center for Mathematics

Sobolev Regularity for Maximal Operators

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Explore recent developments in regularity theory for maximal operators, focusing on Sobolev and BV data. Accessible overview of an active research area with open questions.
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16 Lesons
43 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

The Regularity Problem for the Laplace Equation in Rough Domains

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Explores recent advances in Boundary Value Problems for the Laplace operator in rough domains, focusing on the equivalence between Dirichlet and regularity problem solvability.
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1 Lesons
42 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

A Formula for Sobolev Seminorms Involving Weak L^p

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Explore a mathematical formula for Sobolev seminorms involving weak L^p spaces, presented by Po-Lam Yung from the Hausdorff Center for Mathematics.
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1 Lesons
1 hour
On-Demand
Free-Video
ICTP Mathematics

On the Growth of Sobolev Norms of a Stochastic CGL Equation with Arbitrary Space Dimension

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Explore the growth of Sobolev norms in stochastic CGL equations across arbitrary space dimensions, presented by Guan Huang from Tsinghua University.
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1 Lesons
58 minutes
On-Demand
Free-Video
ICTP Mathematics

Partial Differential Equations - Lecture 25

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Explore advanced concepts in partial differential equations, focusing on complex mathematical theories and their applications in various scientific fields.
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1 Lesons
1 hour 35 minutes
On-Demand
Free-Video
ICTP Mathematics

Partial Differential Equations - Lecture 28

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Explore advanced concepts in partial differential equations, focusing on complex mathematical theories and their applications in various scientific fields.
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1 Lesons
1 hour 29 minutes
On-Demand
Free-Video
ICTP Mathematics

Partial Differential Equations - Lecture 24

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Explore advanced concepts in partial differential equations, focusing on complex mathematical theories and their applications in this comprehensive lecture.
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1 Lesons
1 hour 28 minutes
On-Demand
Free-Video
ICTP Mathematics

Partial Differential Equations - Lecture 22

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Explore advanced concepts in partial differential equations, focusing on complex mathematical theories and their applications in various scientific fields.
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1 Lesons
1 hour 32 minutes
On-Demand
Free-Video
ICTP Mathematics

Partial Differential Equations - Lecture 21

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Explore advanced concepts in partial differential equations, focusing on complex mathematical theories and problem-solving techniques in this comprehensive lecture.
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1 Lesons
1 hour 23 minutes
On-Demand
Free-Video
ICTP Mathematics

Partial Differential Equations - Lecture 16

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Explore advanced concepts in partial differential equations, focusing on complex mathematical theories and problem-solving techniques in this comprehensive lecture.
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1 Lesons
1 hour 27 minutes
On-Demand
Free-Video
ICTP Mathematics

Partial Differential Equations - Lecture 13

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Explore advanced concepts in partial differential equations, focusing on complex mathematical theories and problem-solving techniques in this comprehensive lecture.
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1 Lesons
1 hour 36 minutes
On-Demand
Free-Video
ICTP Mathematics

Partial Differential Equations - Lecture 8

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Explore advanced concepts in partial differential equations, focusing on complex mathematical theories and problem-solving techniques in this comprehensive lecture.
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1 Lesons
1 hour 30 minutes
On-Demand
Free-Video
ICTP Mathematics

Partial Differential Equations - Lecture 10

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Explore advanced concepts in partial differential equations, focusing on complex mathematical theories and problem-solving techniques in this comprehensive lecture.
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1 Lesons
1 hour 33 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Adaptive Wavelet Methods and Applications

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Explore adaptive wavelet methods for solving complex PDEs, including tensor product approximation and reformulation techniques for optimal solutions in various domains.
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1 Lesons
1 hour 26 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

On Density of Sobolev Functions on Euclidean Domains

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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.
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1 Lesons
45 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

New Characterizations of Sobolev Spaces by Po Lam Yung

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Explores novel approaches to characterizing Sobolev spaces, advancing understanding in functional analysis and partial differential equations. Presents cutting-edge research in harmonic analysis.
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1 Lesons
2 hours 7 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Characterisation of Area-Strict Limits of Planar BV Homeomorphisms

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Explore area-strict limits of planar BV homeomorphisms, focusing on cavitations, fractures, and the no-crossing condition in elastic deformations.
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1 Lesons
40 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Plans, Derivations, and Currents in Metric Measure Spaces

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Explore novel proofs and techniques in metric p-Sobolev spaces, connecting plans, derivations, and currents in metric measure spaces. Gain insights into advanced mathematical concepts.
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1 Lesons
42 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Sobolev Spaces in Extended Metric-Topological Measure Spaces

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Explore Sobolev spaces in extended metric-topological measure spaces, focusing on Cheeger energy construction and properties in this general framework.
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1 Lesons
59 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Sobolev Spaces on Metric Spaces - Lecture by Jun Kigami

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Explore Sobolev spaces on metric spaces, covering basic concepts, new examples, and discrete energy. Gain insights into advanced mathematical analysis techniques.
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8 Lesons
32 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Modern Trends in Gagliardo-Nirenberg Inequality

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Explore modern trends in Gagliardo-Nirenberg inequality, including generalizations, refinements, and applications in functional analysis and partial differential equations.
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1 Lesons
26 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Homeomorphic Sobolev Extensions of Parametrizations of Jordan Curves

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Explore homeomorphic Sobolev extensions of Jordan curve parametrizations, examining conditions for finite energy deformations and recent findings in this mathematical field.
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1 Lesons
32 minutes
On-Demand
Free-Video
Institute for Advanced Study

Elliptic Regularity and Singularity

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Explore elliptic regularity and singularity in mathematics with Federico Franceschini's concise talk, gaining insights into advanced mathematical concepts and their applications.
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1 Lesons
16 minutes
On-Demand
Free-Video
NPTEL-NOC IITM

Sobolev Spaces: The Case N = 1 - Part 3

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Explore advanced concepts in Sobolev spaces, focusing on the case N = 1, with Prof. S Kesavan from the Institute of Mathematical Sciences.
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1 Lesons
20 minutes
On-Demand
Free-Video
NPTEL-NOC IITM

Sobolev Spaces: Density of Test Functions in Euclidean Space - Part 2

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Explore density of test functions in Sobolev spaces on Euclidean space, advancing understanding of mathematical analysis.
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1 Lesons
15 minutes
On-Demand
Free-Video
NPTEL-NOC IITM

Sobolev Spaces: Definition, Notations, and Completeness - Part 1

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Explore Sobolev spaces: definition, notations, and completeness. Gain foundational knowledge in this essential mathematical concept for advanced analysis.
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1 Lesons
33 minutes
On-Demand
Free-Video
NPTEL-NOC IITM

Weak Solutions of Elliptic Boundary Value Problems - Part 1

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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.
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1 Lesons
29 minutes
On-Demand
Free-Video
BIMSA

Function Spaces on Quantum Tori and Their Applications

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Explore Sobolev, Besov, and Triebel-Lizorkin spaces on quantum tori, examining their properties and applications in pseudo-differential theory and noncommutative geometry.
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1 Lesons
53 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

The Computational Theory of Riemann-Hilbert Problems - Lecture 4

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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.
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25 Lesons
1 hour 1 minute
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Flows of Irregular Vector Fields in Fluid Dynamics - Lecture 6

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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.
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1 Lesons
1 hour 45 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Flows of Irregular Vector Fields in Fluid Dynamics - Lecture 5

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Explore modern techniques for analyzing flows of irregular vector fields, including quantitative regularity estimates, nonuniqueness solutions, and applications to fluid dynamics PDEs.
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1 Lesons
1 hour 55 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Flows of Irregular Vector Fields in Fluid Dynamics - Lecture 4

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Explore modern techniques for analyzing flows of irregular vector fields, including quantitative regularity estimates, nonuniqueness solutions, and applications to fluid dynamics PDEs.
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1 Lesons
1 hour 54 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Flows of Irregular Vector Fields in Fluid Dynamics - Lecture 3

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Explore modern techniques for analyzing flows of irregular vector fields, including quantitative regularity estimates, nonuniqueness solutions, and applications to fluid dynamics PDEs.
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1 Lesons
1 hour 47 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Flows of Irregular Vector Fields in Fluid Dynamics - Lecture 2

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Explore modern techniques for analyzing flows of irregular vector fields, including quantitative regularity estimates, nonuniqueness solutions, and applications to fluid dynamics PDEs.
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1 Lesons
1 hour 48 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Flows of Irregular Vector Fields in Fluid Dynamics - Lecture 1

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Explore modern concepts in flows of irregular vector fields, including quantitative regularity estimates, nonuniqueness solutions, and applications to fluid dynamics and turbulence theory.
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1 Lesons
1 hour 46 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Minimization Problems for the Axisymmetric Neo-Hookean Energy

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Explore minimization problems for axisymmetric neo-Hookean energy, focusing on existence of minimizers, energy concentration, and bounds for relaxed energy in critical Sobolev cases.
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1 Lesons
38 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Weakly Turbulent Solution to the Schrödinger Equation on the 2D Torus with Potential

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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.
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1 Lesons
30 minutes
On-Demand
Free-Video
Society for Industrial and Applied Mathematics

Advection-Diffusion Problems on Polygonal Meshes

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Explore advanced mathematical techniques for solving advection-diffusion PDEs on polygonal meshes, covering high-order finite elements, WENO methods, and practical applications in geosciences.
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3 Lesons
1 hour
On-Demand
Free-Video