Organisers: Lucio Boccardo (Sapienza Università di Roma), Florica-Corina Cîrstea (University of Sydney), Julie Clutterbuck (Monash University), L. Craig Evans (University of California, Berkeley), Enrico Valdinoci (University of Melbourne), Paul Bryan (University of Queensland)

Key Speakers:
The lecture series will be given by three prominent researchers:

Neil Trudinger (ANU) is known particularly for his work in the field of nonlinear elliptic partial differential equations. After completing his B.Sc at the University of New England (Australia) in 1962, he continued his graduate studies at Stanford University. He was awarded a Ph.D in 1966 for his thesis “Quasilinear elliptical partial differential equations in n variables”. He is the author, together with David Gilbarg, of Elliptic Partial Differential Equations of Second Order, which was awarded the Leroy P. Steele Prize for Mathematical Exposition by the American Mathematical Society in 2008.

Valentina Wheeler (UoW) received her PhD with her dissertation titled, ‘Mean curvature flow of graphs with free boundaries’ from Freie Universität Berlin, Germany in 2011. Her research interest includes geometric analysis, geometric evolution equations, and partial differential equations. She will lecture on Mean Curvature Flow (MCF) with Free boundaries (Abstract).

Connor Mooney (ETH Zurich) is a postdoctoral researcher at ETH Zurich since 2016. He received his PhD from Columbia University in 2015. In his talk, he will discuss some classical results of the regularity for minimizers of convex functionals in the calculus variations, and continue on some more recent results and open questions when the functional is degenerate convex, or the minimizer is vector-valued.

Topics include: C^{1,alpha} estimates in dimension 2 when the functional is uniformly convex (a simple proof in scalar case with maximum principle, then Morrey’s energy estimates); De Giorgi-Nash in the higher-dimensional scalar case, counterexamples to De Giorgi-Nash technique in the vector-valued case; Parabolic analogues of the above (Necas-Sverak theorem in the case n = 2, counterexample to linear estimates when n,m > 1 (M.), open questions); C^1 regularity when functional is degenerate and n = 2 (De Silva-Savin), open questions in higher-dimensional case; and Counterexamples to C^1 regularity of minimizers when n>1 and m > 1 (Sverak-Yan, M.-Savin)

During the week there will be opportunities for participants to talk about their research, and collaborate with colleagues.

Program Details and Materials:
Below is the Program Structure. Please click to enlarge.

Registration deadline: 24 September 2017

• You are invited to attend week one (Graduate lecture series) of the Elliptic partial differential equations of second order: Celebrating 40 years of Gilbarg and Trudinger’s book MATRIX program.
• There will be some opportunities for participants to give a 25 minute talk about their current research.  If you would like to propose a talk, please enter the title upon registration.
• Registration is by invitation only and place is limited. Attendance will be confirmed once the registration is closed.
• Only one registration is required. Please indicate your dates of attendance and add all events to the Event Cart before checkout.

Participant List:

• Julie Clutterbuck (Monash University)
• Connor Mooney (ETH Zurich)
• Mariel Sáez (Pontificia Universidad Católica de Chile)
• Neil Trudinger (Australian National University )
• Valentina Wheeler (University of Wollongong)
• Sophie Chen (Australian National University)
• Yanqin Fang (University of Wollongong)
• Calum Robertson (Monash University)
• Stefano Vita (Università di Torino, Politecnico di Torino)
• Giorgio Tortone (Università di Torino)
• Ting-Ying Chang (Monash University)
• Hadil Alhazmi (Australian National University)
• Haodi Chen (Australian National University)
• Julian Bailey (Australian National University)
• Leslie Cheung (University of Queensland)
• Alessandro Audrito (Università di Torino)

ASSOCIATED EVENTS

Elliptic partial differential equations of second order: Celebrating 40 years of Gilbarg and Trudinger’s book  
16 October to 28 October 2017