PAST SCIENTIFIC EVENTS WHERE ORGANIZERS, PARTICIPANTS AND COLLABORATORS WERE INVOLVED

[1] WCNA 2008
Four-session-Minisymposium on Harnack Inequalities in Analysis and Partial Differential Equations
July 2 - 9, 2008 in Orlando, Florida (USA)
Session Organizers: Ugur Abdulla, Emmanuele DiBenedetto, Ugo Gianazza, Patrick Guidotti, John Lewis, Juan Manfredi, Gieri Simonett, Vincenzo Vespri.

[2] SIAM Conference on Analysis of Partial Differential Equations, (USA)
Minisymposium on Recent Development in Nonlinear Degenerate Elliptic and Parabolic Equations, Potential Theory and Applications, Part I and Part II
December 10 - 12, 2007 in Mesa, Arizona (USA)

[3] 2007 Workshop/Summer School in Saariselkä (Finland)
Qualitative Properties of Solutions to Elliptic and Parabolic Equations
European Science Foundation Programme
June 7 - 10, 2007 in Saariselkä, Finland
In his talk, John Lewis discussed joint work with Kaj Nyström concerning the Martin boundary problem for p-harmonic functions in a Lipschitz domain and the corresponding question of when a minimal positive p-harmonic function (with respect to a given boundary point) is unique up to constant multiples. In particular he outlined a proof that shows the Martin boundary can be identified with the topological boundary in domains that are convex or C¹. The proof depends on several recent boundary Harnack inequalities of the authors for the ratio of two positive p-harmonic functions, vanishing on a portion of the boundary of a Lipschitz domain. Thus these inequalities were discussed in detail.
Juan Manfredi presented a communication, where he first surveyed some recent results on p-harmonic measure including recent developments by Björn-Björn-Shanmugalingam and Llorente-Manfredi-Wu. He continued with a version of a fundamental Lemma of Tom Wolff on the failure of the mean-value property for p-harmonic functions in the unit disk obtained in collaboration with Harri Varpanen.
In his 4-hour-minicourse Ugo Gianazza presented some recent results, obtained in joint papers with Emmanuele DiBenedetto and Vincenzo Vespri. He first established the intrinsic Harnack inequality for non-negative solutions of a class of degenerate, quasilinear, parabolic equations, including equations of the p-Laplacean and porous medium type. He showed that the classical Harnack estimate, while failing for degenerate parabolic equations, it continues to hold in a space-time geometry intrinsic to the degeneracy. The proof uses only measure-theoretical arguments and it reproduces the classical Moser theory for non-degenerate equations. Hölder estimates will be derived as a consequence of the Harnack inequality. Then he showed that non-negative weak solutions of quasilinear degenerate parabolic equations of p-Laplacean type are locally bounded below by Barenblatt type sub-potentials. These lower bounds permit one to recast the previously proved Harnack inequality in a family of alternative, equivalent forms. Finally he discussed Harnack inequalities for non-negative solutions of a class of singular, quasilinear, parabolic equations. Once more these classes of singular equations include the p-Laplacean equation and equations of the porous medium type.


[4] SIAM Conference on Analysis of Partial Differential Equations (USA)
Minisymposium on Recent Development in the Theory of Nonlinear Degenerate Elliptic and Parabolic Equations with Applications
July 10 - 12, 2006 in Boston, Massachusetts (USA)