Eikonal rendering
Eikonal Rendering
©   http://www.mpi-inf.mpg.de/resources/EikonalRendering/index.html



Jump to:

Vladimir Tkachev's Homepage

Matematisa institutionen, UU

FMB

Schemasökning, UU




Back Back

Lecture notes and materials

horizontal rule


    Week I

  1. 2008-09-23:  Introduction. 1st order PDE. Characteristics.

  2. 2008-09-24:  Eikonal equation. Burger's equation. Weak solutions.

  3. 2008-09-25:  Hamilton-Jacobi equation. Hopf-Lax formula.

  4. 2008-09-26:  Distributions and weak derivatives

  5. 2008-09-26:  Exercises, part I

    Week II

  6. 2008-10-07:  Sobolev spaces: basic definitions

  7. 2008-10-08:  Elementary elliptic equations and existence of weak solutions

  8. 2008-10-09:  Sobolev inequalities and embedding theorems

  9. 2008-10-10:  Maximum principles

  10. 2008-10-10:  Exercises, part II

    Week III

  11. 2008-10-22:  Inner regularity for elliptic PDE (an updated version)

  12. 2008-10-23:  Elliptic equations: some classical applications

  13. 2008-10-24:  Conservations laws: systems and admissibility conditions






Here is some useful links to subjects I talked about on lectures (optional)

Convexity and beyond
  • Convex Optimization Boyd and Vandenberghe
    ... - Sobolev - Topology - Knots - Geometry - ...
  • Some general remarks on topological connections, see, for instance Hodge decomposition in Wiki on de Rham cohomology
  • S. Donaldson's surveys on four-dimensional topology Mathematical uses of gauge theory and Yang-Mills theory and geometry
  • see also Mobius energy of knots and unknots and Divergence-free fields: energy and asymptotic crossing number by M. H. Freedman and Zh. He



  • Non-commutative geometry and Alian Connes book (see also Noncommutative Geometry for Pedestrians by J. Madore)
  • Differential Equations. Function Spaces. Approximation Theory dedicated to the 100th anniversary of the birthday of Sergei L. Sobolev

    •