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AMCS Short Course: The C^p’ regularity conjecture in the plane

Start Date: January 6, 2019
End Date: January 8, 2019

By Prof. José Miguel Urbano (University of Coimbra, in Portugal)
Geometric tangential analysis refers to a constructive systematic approach to quantitative estimates based on the concept that a problem which enjoys greater regularity can be tangentially accessed by certain classes of pdes. By means of iterative arguments, the method then imports this regularity, properly corrected through the path used to access the tangential equation, to the original class. Using these ideas, we will prove the planar counterpart of the longstanding conjecture that solutions of the degenerate p-Poisson equation with a bounded source have derivatives which are locally Hölder continuous with exponent p'; this regularity is optimal
Bio: José Miguel Urbano is a Professor of Mathematics at the University of Coimbra, in Portugal. He has studied in Paris (École Polytéchnique, 1995), Lisbon (PhD, 1998) and Chicago (postdoc, Northwestern University, 1999). He is the author of the book "The Method of Intrinsic Scaling”, published in the series Lecture Notes in Mathematics, and of over 50 scientific papers in the area of Nonlinear Partial Differential Equations. He has supervised four PhD students and ten postdoctoral fellows and has taught short courses at IMPA (Brazil), the University of Florence (Italy), Aalto University (Finland) the Federal University of Ceará (Brazil) and KAUST (Saudi Arabia). He was invited speaker in several international conferences and served in panels for the evaluation of grants and research projects for the EU, the ERC, the Academy of Finland and the Portuguese Science Foundation. He is an associate editor of the journal "Nonlinear Analysis”.

More Information:

For more info contact: Prof. Diogo Gomes: email:
Date: Sunday 6 Jan,Monday 7 Jan,Tuesday 8 Jan 2019 
Time:03:00 PM - 04:30 PM
Location: Location: Building 1,Level 3,Room 3119
Refreshments: will be provided