Lester L. Helms--Home Page

 
Emeritus Professor,  Department of Mathematics
 University of Illinois at Urbana-Champaign
1409 W. Green Street
Urbana, Illinois 61801

Home Address: 2509 Pond Street, Urbana, IL 61801
Telephone: 217 344 4821
e-mail:  l-helms@math.uiuc.edu

General Information
Ph. D., Purdue University, 1956

Mathematical Interests

My interests lie in three interrelated topics: heat equations associated with second-order elliptic operators, Markov or diffusion processes, and potential theory. In the early 1950s, W. Feller characterized one-dimensional diffusions by representing their infinitesimal generators intrinsically and determined all possible boundary conditions. In 1959, Ventcel characterized the infinitesimal generators of general diffusion processes on bounded domains in higher dimensions as a second-order elliptic operator subject to boundary conditions involving diffusion, absorption, reflection, and viscosity at the boundary. The problem of showing that a second-order elliptic operator subject to such boundary conditions generates a Markov or diffusion process is in its infancy. The best results obtained so far involve a nondegenerate second-order elliptic operator subject to oblique derivative boundary conditions.
 
Selected Publications and Comments

Preprint: Diffusions with Absorption and Reflection (PDF file)

Books

  1. An Introduction to Potential Theory, Wiley-Interscience, New York, 1969. (German translation: Walter de Gruyter, 1973)
  2. Introduction to Probability Theory with Contemporary Applications, W.H. Freeman, 1996. (Reprinted by Dover Publications, Inc., 1997)
  3. Potential Theory, Springer-Verlag, London, 2009
Ph.D. Students
  1. Marvin Grossman, 1963
  2. Richard Griego, 1965
  3. Talma Leviatan, 1970
  4. James Frykman, 1975
  5. Carla Neaderhouser Purdy, 1975
  6. Robert Bonvallet, 1979
Last revised: April 26, 2011