Boundary Value Problems for Degenerate Elliptic Equations

*(Invited Minisymposium)*

10:45 AM-12:45 PM

*Room: Atlanta 3*

Degenerate elliptic equations arise in a number of continuum problems. Perhaps the best known is the porous medium equation, representing flow in a medium whose diffusivity depends on saturations. The medium may be isotropic or anisotropic; in either case, free boundary problems occur. Recent work on self-similar solutions of multidimensional conservation laws provides another source of such problems: the degeneracy is typically anisotropic, and mathematical results are just now being developed. The speakers in this minisymposium will discuss proved existence of solutions that change sign for a quasilinear model problem, positive solutions to an anisotropic problem, results on conservation law models and their application to weak shock reflection and the von Neumann paradox, and regularity results for a linear anisotropically degenerate equation.

**Organizer: Barbara L. Keyfitz**

*University of Houston*

**10:45-11:10 Sign-Changing Solutions to Singular Second-Order Boundary Value**

- P. J. McKenna, University of Connecticut, Storrs

**11:15-11:40 Positive Solution to Anisotropic Quasilinear Elliptic Equations**

*Y .S. Choi*and E. H. Kim, University of Connecticut, Storrs

**11:45-12:10 On a Degenerate Elliptic Equation Arising in Weak Shock Reflection**

- Suncica Canic, University of Houston

**12:15-12:40 The Regularity of a Singular Equation**

- Yi Li and Lihe Wang, University of Iowa

*LMH, 1/19/99, MMD, 1/26/99*