Daniel Daners: Personal Front Page

General Information

I am an Associate Professor in the School of Mathematics and Statistics at The University of Sydney.

Contact Information

A/Prof Daniel Daners School of Mathematics and Statistics F07 The University of Sydney, NSW 2006 Australia   Office: Carslaw Building Room 715 Phone: +61 2 9351 2966 Fax: +61 2 9351 4534 Email: daniel.daners@sydney.edu.au

Research

I am a member of the Nonlinear Analysis Group. My interests are partial differential equations (particularly elliptic and parabolic boundary value problems), dynamical systems, analytic semigroup theory, operator theory.

Publication Highlights

Recent publications: (posted 29 Jan 2013):

• Non-positivity of the semigroup generated by the Dirichlet-to-Neumann operator, Preprint, January 2013, to appear in Positivity.
• Eigenvalue problems for a cooperative system with a large parameter, Advanced Nonlinear Studies 13 (2013), 137-148.
• with AP Campbell, Linear algebra via complex analysis, Preprint, April 2012, to appear in American Mathematical Monthly (general interest).

Below some publication highlights. You can also look at my complete list of publications including preprints and links to the original articles if available or view the 10 most frequently cited publications in MathSciNet.

• with P Koch Medina, Abstract evolution equations, periodic problems and applications, Longman Scientific & Technical, Harlow, Essex, 1992.
• Domain perturbation for linear and semi-linear boundary value problems, Handbook of Differential Equations: Stationary Partial Differential Equations, Vol 6, (2008), 1-81, Elsevier, 2008. ISBN-13: 978-0-444-53241-1.
• A Faber-Krahn inequality for Robin problems in any space dimension, Mathematische Annalen, 335 (2006), 767 - 785. (improvements with uniqueness and for p-Laplacian)
• Dirichlet problems on varying domains, J Diff Eq 188 (2003), 591-624. (related work)
• Heat kernel estimates for operators with boundary conditions, Math Nachr, 217(2000), 13-41.
• Robin boundary value problems on arbitrary domains, Trans AMS, 352 (2000), 4207-4236. (related work)
• with EN Dancer, Domain perturbation for elliptic equations subject to Robin boundary conditions, J Diff Eq 138 (1997), 86-132.
• Domain perturbation for linear and nonlinear parabolic equations, J Diff Eq 129 (1996), 358-402. (related work)

Professional Activities

• Organiser of 57th Annual Meeting of the Australian Mathematical Society at the University of Sydney
• Organiser of the Tohoku-Sydney Workshop on nonlinear PDE's for early career researchers on March 9, 2012 (joint with Tohoku Unversity)
• I help organise the AMSI-ANU Workshop on Spectral Theory (July 13-17, 2009)
• Organiser of special ession at the 7th Australia & New Zealand Mathematics Convention (with Yihong Du and Tom ter Elst)
• Organiser of special ession at the 50th Annual Meeting of the Australian Mathematical Society (with Xuan Duong and Xu-Jia Wang)
• Organiser of ICE-EM/AMSI Summer School 2007 (with Ruibin Zhang and Georg Gottwald)
• Organiser of conference Recent Advances in Nonlinear Partial Differential Equations at the University of New England from 16-21 July 2006 (with Yihong Du and Shusen Yan)

Courses Taught Recently

• MATH1903: Integral Calculus and Modelling
• MATH1906: Mathematics Special Studies Program
• MATH2961: Linear Algebra and Vector Calculus (Advanced)
• MATH2962: Real and Complex Analysis (Advanced)
• MATH3969: Measure Theory and Fourier Analysis (Advanced)

I am the coordinator for the first and second year Mathematics Special Studies Program (MATH1906/MATH1907 as well as MATH2916/MATH2917) and the Mathematics Talented Student Program.

You can also view my current lecture and tutorial timetable including my consultation hour (during the semester only).