Differential Analysis, Spring 2004, MIT

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25 Papers | 1 Member | Created by Bar tender on 8/22/2008 | Category: Analysis

Description: The main goal of this course is to give the students a solid foundation in the theory of elliptic and parabolic linear partial differential equations. It is the second semester of a two-semester, graduate-level sequence on Differential Analysis.

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0 - Course Overview; Examples of Harmonic Functions; Fundamental Solutions for Laplacian and Heat Operator

By Bar tender August 22, 2008

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Category: Analysis

Tags: FUNCTIONS Harmonic heat Laplacian Operator

9- If Delta u in C^{alpha}, alpha 0, then u in C^{2}; Moreover, if alpha 1, then u in C^{2,alpha}

By Bar tender August 22, 2008

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10 - Interior C^{2,alpha} Estimate for Newtonian Potential; Interior C^{2,alpha} Estimates for Poisson's Equation; Boundary Estimate on Newtonian Potential: C^{2,alpha} Estimate up to the Boundary for Domain with Flat Boundary Portion

By Bar tender August 22, 2008

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11 -Schwartz Reflection Reviewed; Green's Function for Upper Half Space Reviewed

By Bar tender August 22, 2008

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Category: Analysis

Tags: Hölder Norms Schwartz

12 - Global C^{2,alpha} Solution of Poisson's Equation Delta u = f in C^{alpha}, for C^{2,alpha} Boundary Values in Balls; Constant Coefficient Operators; Interpolation between Hölder Norms

By Bar tender August 22, 2008

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Category: Analysis

Tags: Coefficient

13 - Interior Schauder Estimate

By Bar tender August 22, 2008

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Category: Analysis

Tags: Interior Schauder

14 - Global Schauder Estimate; Banach Spaces and Contraction Mapping Principle

By Bar tender August 22, 2008

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Category: Analysis

Tags: Banach Contraction Schauder

15 - Continuity Method; Can Solve Dirichlet Problem for General L; Provided can Solve for Laplacian Corollary Solution of

By Bar tender August 22, 2008

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Category: Analysis

Tags: Dirichlet General L Laplacian

16 - Elliptic Regularity: If f and Coefficients of L in C^{k,alpha}, Lu = f, then u in C^{k+2,alpha}; C^{2,alpha} Regularity up to the Boundary

By Bar tender August 22, 2008

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Category: Analysis

Tags: Dirichlet General L Laplacian

17 - Hilbert Spaces and Riesz Representation Theorem; Weak Solution of Dirichlet Problem for Laplacian in W^{1,2}_0; Weak Derivatives; Sobolev Spaces

By Bar tender August 22, 2008

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Category: Analysis

Tags: derivatives Hilbert Laplacian Sobolev weak

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