Wednesday, December 12

MS48
Recent Development in Nonlinear Degenerate Elliptic and Parabolic Equations, Potential Theory and Applications - Part I of II

10:30 AM - 1:00 PM
Room: Poblano

For Part II, see MS53

This minisymposium reflects recent important developments made in the theory and applications of the nonlinear degenerate and singular elliptic and parabolic equations. The new intrinsic form Harnack Estimates for the non-negative solutions of quasi-linear degenerate parabolic equations with the measurable coefficients, the new boundary Harnack inequality for the p-Harmonic functions, Wiener's criterion for the regularity of the point at infinity and its measure-theoretical, probabilistic and potential theory counterparts will be presented.

Organizer: Ugur G. Abdulla
Florida Institute of Technology
Emmanuele DiBenedetto
Vanderbilt University

10:30-10:55 Connecting Non--Negative Solutions to Quasi--Linear Degenerate Equations, Sub-potentials

Emmanuele DiBenedetto, Vanderbilt University

11:00-11:25 Wiener's Criterion for the Regularity of the Point at Infinity and its Measure-Theoretical Counterpart

Ugur G. Abdulla, Florida Institute of Technology

11:30-11:55 Beyond the Laplacian

John Lewis, University of Kentucky

12:00-12:25 Continuity of the Saturation in the Flow of Two Immiscible Fluids Through a Porous Medium

Ugo P. Gianazza, University of Pavia, Italy; Emmanuele DiBenedetto, Vanderbilt University; Vincenzo Vespri, University of Florence, Italy

12:30-12:55 On the Regularity of the Free Boundary for the Classical Stefan Problem

Jan Prüss, Martin-Luther-Universität, Germany; Jürgen Saal, University of Konstanz, Germany; Gieri Simonett, Vanderbilt University