Professor Neil Trudinger
BSc(Hons),UNE, MS,PhD, Stanford, FAA,FRS.
Emeritus Professor
ANU College of Science
Areas of expertise
- Partial Differential Equations 010110
Publications
- Trudinger, N 2021, 'On the local theory of prescribed Jacobian equations revisited', Mathematics in Engineering, vol. 3, no. 6, pp. 1-17.
- Trudinger, N 2020, 'Remarks on the Pucci Conjecture', Indiana University Mathematics Journal, vol. 69, no. 1, pp. 109-118.
- Jiang, F & Trudinger, N 2020, 'On the Dirichlet problem for general augmented Hessian equations', Journal of Differential Equations, vol. 269, no. 6, pp. 5204-5227.
- Jiang, F & Trudinger, N 2019, 'Oblique boundary value problems for augmented Hessian equations III', Communications in Partial Differential Equations, vol. 44, no. 8, pp. 708-748.
- Jiang, F & Trudinger, N 2018, 'On the Second Boundary Value Problem for Monge-Ampère Type Equations and Geometric Optics', Archive for Rational Mechanics and Analysis, vol. 229, pp. 547-567pp.
- Jiang, F & Trudinger, N 2018, 'Oblique boundary value problems for augmented Hessian equations I', Bulletin of Mathematical Sciences, vol. 8, no. 2, pp. 353-411pp.
- Jiang, F & Trudinger, N 2017, 'Oblique boundary value problems for augmented Hessian equations II', Nonlinear Analysis, vol. 154, pp. 148-173pp.
- Jiang, F, Trudinger, N & Xiang, N 2016, 'On the Neumann problem for Monge-Ampère type equations', Canadian Journal of Mathematics, vol. 68, no. 6, pp. 1334-1361.
- Liu, J & Trudinger, N 2016, 'On the classical solvability of near field reflector problems', Discrete and Continuous Dynamical Systems, Series A, vol. 36, no. 2, pp. 895-916pp.
- Jiang, F, Trudinger, N & Yang, X 2015, 'On the Dirichlet problem for a class of augmented Hessian equations', Journal of Differential Equations, vol. 258, no. 5, pp. 1548-1576.
- Liu, J, Trudinger, N & Wang, X 2015, 'On Asymptotic Behaviour and W-2,W-p Regularity of Potentials in Optimal Transportation', Archive for Rational Mechanics and Analysis, vol. 215, no. 3, pp. 867-905.
- Jiang, F & Trudinger, N 2014, 'On Pogorelov estimates in optimal transportation and geometric optics', Bulletin of Mathematical Sciences, vol. 4, no. 3, pp. 407-431.
- Jiang, F, Trudinger, N & Yang, X 2014, 'On the Dirichlet problem for Monge-Ampère type equations', Calculus of Variations and Partial Differential Equations, vol. 49, no. 3-4, pp. 1223-1236.
- Trudinger, N & Zhang, W 2014, 'Weak continuity of the complex k-hessian operators with respect to local uniform convergence', Bulletin of the Australian Mathematical Society, vol. 89, no. 2, pp. 227-233.
- Trudinger, N 2014, 'On the local theory of prescribed Jacobian equations', Discrete and Continuous Dynamical Systems, Series A, vol. 34, no. 4, pp. 1663-1681.
- Trudinger, N & Zhang, W 2013, 'Hessian measures on the Heisenberg group', Journal of Functional Analysis, vol. 264, no. 10, pp. 2335-2355.
- Trudinger, N 2013, 'A note on global regularity in optimal transportion', Bulletin of Mathematical Sciences, vol. 3, no. 3, pp. 551-557.
- Sheng, W, Trudinger, N & Wang, X 2012, 'Prescribed Weingarten Curvature Equations', in Yuxin Dong; Jixiang Fu; Guozhen Lu; Weimin Sheng; Xiaohua Zhu (ed.), Recent Developments in Geometry and Analysis, International Press, USA, pp. 359-386.
- Sheng, W, Trudinger, N & Wang, X 2012, 'The k-Yamabe problem', in Huai-Dong Cao; Shing-Tung Yau (ed.), Surveys in Differential Geometry Volume 17, International Press, USA, pp. 427-457.
- Dai, Q, Trudinger, N & Wang, X-J 2012, 'The mean curvature measure', Journal of European Mathematical Society, vol. 14, no. 3, pp. 779-800.
- Trudinger, N 2011, 'On generated prescribed Jacobian equations', Partial Differential Equations, ed. G Huisken, EMS Publishing House, Zurich Switzerland, pp. 2194-2189.
- Liu, J & Trudinger, N 2010, 'On Pogorelov estimates for Monge-Ampère type equations', Discrete and Continuous Dynamical Systems, Series A, vol. 28, no. 3, pp. 1121-1135.
- Liu, J, Trudinger, N & Wang, X-J 2010, 'Interior C 2,alpha regularity for potential functions in optimal transportation', Communications in Partial Differential Equations, vol. 35, no. 1, pp. 165-184.
- Maugeri, A, Venkatesha Murthy, M & Trudinger, N 2008, 'Journal of Global Optimization: Preface', Journal of Global Optimization, vol. 40, no. 1-3, pp. 1-5.
- Trudinger, N & Wang, X-J 2010, 'The intermediate case of the Yamabe problem for higher order curvatures', International Mathematics Research Notices, vol. 227, pp. 1-22.
- Kuo, H & Trudinger, N 2009, 'On the Krylov maximum principle for discrete parabolic schemes', Tamkang Journal of Mathematics, vol. 40, no. 4, pp. 437-450.
- Guan, P, Ma, X, Trudinger, N et al 2009, 'A Form of Alexandrov-Fenchel Inequality', Pure and Applied Mathematics Quarterly, vol. 6, no. 3, pp. 999-1012.
- Trudinger, N & Wang, X-J 2009, 'On Harnack inequalities and singularities of admissible metrics in the Yamabe problem', Calculus of Variations and Partial Differential Equations, vol. 35, no. 3, pp. 317-338.
- Trudinger, N & Wang, X-J 2009, 'On strict convexity and continuous differentiability of potential functions in optimal transportation', Archive for Rational Mechanics and Analysis, vol. 192, no. 3, pp. 403-418.
- Trudinger, N & Wang, X-J 2009, 'On the second boundary value problem for Monge-Ampere type equations and optimal transportation', Annali Della Scuola Normale Superiore di Pisa, vol. 8, no. 1, pp. 143-174.
- Trudinger, N & Wang, X-J 2009, 'Quasilinear Elliptic Equations with Signed Measure Data', Discrete and Continuous Dynamical Systems, Series A, vol. 23, no. 1 & 2, pp. 477-494.
- Kuo, H & Trudinger, N 2008, 'On the maximum principle for linear parabolic equations', Journal of Global Optimization, vol. 40, no. 3, pp. 495-500.
- Trudinger, N 2008, 'On the Prescribed Jacobian Equation', International Conference for the 25th Anniversary of Viscosity Solutions, ed. Y Giga; K Ishii; S Koike; T Ozawa; N Yamada, Gakuto International Series, Tokyo, Japan, pp. 243-255.
- Trudinger, N & Wang, X-J 2008, 'Boundary regularity for the Monge-Ampere and affine maximal surface equations', Annals of Mathematics, vol. 167, no. 3, pp. 993-1028.
- Trudinger, N & Wang, X-J 2008, 'The Monge-Ampere equation and its geometric applications', in Lizhen Ji; Peter Li; Richard Schoen; Leon Simon (ed.), Handbook of Geometric Analysis (Volume 1), Higher Education Press, Somerville, USA, pp. 467-524.
- Trudinger, N 2007, 'Recent developments in the theory of nonlinear elliptic partial differential equations', in M.Sanz-Sole, J.Soria, J.L.Varona, J.Verdera (ed.), Proceedings of the International Congress of Mathematicians, Madrid 2006 - Invited Lectures, American Mathematical Society, Germany, pp. 291-302.
- Kuo, H & Trudinger, N 2007, 'New maximum principles for linear elliptic equations', Indiana University Mathematics Journal, vol. 56, no. 5, pp. 2439-2452.
- Sheng, W, Trudinger, N & Wang, X-J 2007, 'The Yamabe problem for higher order curvatures', Journal of Differential Geometry, vol. 77, pp. 515-553.
- Trudinger, N 2006, 'On Hessian Measures for Non-Commuting Vector Fields', Pure and Applied Mathematics Quarterly, vol. 2, no. 1, pp. 147-161.
- Sheng, W, Trudinger, N & Wang, X-J 2006, 'Enclosed convex hypersurfaces with maximal affine area', Mathematische Zeitschrift, vol. 252, pp. 497-510.
- Trudinger, N 2006, 'Recent developments in elliptic partial differential equations of Monge-Ampere type', International Congress of Mathematicians, Madrid, European Mathematical Society, vol. 3, pp. 291-312.
- Chaudhuri, N & Trudinger, N 2005, 'An Alexandrov type theorem for k-convex functions', Bulletin of the Australian Mathematical Society, vol. 71, no. 2, pp. 305-314.
- Kuo, H & Trudinger, N 2005, 'Estimates for solutions of fully nonlinear discrete schemes', in J Rodrigues et al. (ed.), Trends in partial differential equations of mathematical physics, Birkhauser Verlag, Switzerland, pp. 275-282.
- Trudinger, N & Wang, X-J 2005, 'The affine Plateau problem', Journal of the American Mathematical Society, vol. 18, no. 2, pp. 253-289.
- Trudinger, N, Ma, X & Wang, X-J 2005, 'Regularity of Potential Functions of the Optimal Transportation Problem', Archive for Rational Mechanics and Analysis, vol. 177, pp. 151-183.
- Trudinger, N 2004, 'The Chern Conjecture in Affine geometry', International Congress of Chinese Mathematicians (ICCM 2001), ed. CS Lin, Lo Yang and ST Yau, International Press, USA, pp. 25-30.
- Ivochkina, N, Trudinger, N & Wang, X-J 2004, 'The Dirichlet Problem for degenerate Hessian Equations', Communications in Partial Differential Equations, vol. 29, pp. 219-235.
- Ivochkina, N, Trudinger, N & Wang, X-J 2005, 'The Dirichlet Problem for Degenerate Hessian Equations', Communications in Partial Differential Equations, vol. 29, no. 1&2, pp. 219-235.
- Sheng, W, Trudinger, N & Wang, X-J 2004, 'Convex hypersurfaces of prescribed Weingarten curvatures', Communications in Analysis and Geometry, vol. 12, no. 1, pp. 213-232.
- Trudinger, N & Sheng, W 2003, 'On the affine diameter of closed convex hypersurfaces', Bulletin of the Australian Mathematical Society, vol. 68, no. 3, pp. 431-437.
- Kuo, H & Trudinger, N 2002, 'Schauder estimates for fully nonlinear elliptic difference operators', Proceedings of the Royal Society of Edinburgh, vol. 132A, pp. 1395-1406.
- Trudinger, N & Wang, X-J 2002, 'Affine complete locally convex hypersurfaces', Inventiones Mathematicae, vol. 150, pp. 45-60.
- Trudinger, N & Wang, X-J 2002, 'Bernstein-Jorgens Theorem for a Fourth Order Partial Differential Equation', Journal of Partial Differential Equations, vol. 15, no. 1, pp. 78-88.
- Trudinger, N & Wang, X-J 2002, 'Hessian Measures III', Journal of Functional Analysis, vol. 193, pp. 1-23.
- Trudinger, N & Wang, X-J 2002, 'On locally convex hypersurfaces with boundary', Journal fur Reine und Angewandte Mathematik, vol. 551, pp. 11-32.
- Trudinger, N & Wang, X-J 2002, 'On the weak continuity of Elliptic Operators and applications to Potential Theory', American Journal of Mathematics, vol. 124, no. 2, pp. 369-410.
- Trudinger, N 2001, 'Glimpses of nonlinear partial differential equations in the Twentieth century. A Priori estimates and the Bernstein problem', in Chen L H Y, Jesudason J P, Lai C H, Oh C H, Phua K K, Tan E-C (ed.), Challenges for the 21st Century: International Conference on Fundamental Sciences: Mathematics and Theoretical Physics, World Scientific Publishing Company, Singapore, pp. 196-212.
- Trudinger, N & Wang, X-J 2001, 'On the Monge mass transfer problem', Calculus of Variations and Partial Differential Equations, vol. 13, pp. 19-31.
- Kuo, H & Trudinger, N 2000, 'A note on the discrete Aleksandrov-Bakelman maximum principle', Taiwanese Journal of Mathematics, vol. 4, no. 1, pp. 55 - 64.
- Trudinger, N & Wang, X-J 2000, 'The Bernstein problem for affine maximal hypersurfaces', Inventiones Mathematicae, vol. 140, no. 2, pp. 399 - 422.
- Guan, P., Trudinger, N, & Wang, X.-J 1999, 'On the Dirichlet problem for degenerate Monge-Amp\`ere equations', Acta Mathematica, vol. 182, no. 1, pp. 87-104.
- Trudinger, N & Wang, X-J 1999, 'Hessian Measures II', Annals of Mathematics, vol. 150, no. 2, pp. 579-604.
- Trudinger, N 1995, 'On the Dirichlet problem for Hessian equations', Acta Mathematica, vol. 175, pp. 151-164.
Projects and Grants
Grants information is drawn from ARIES. To add or update Projects or Grants information please contact your College Research Office.
- Singularity and regularity for Monge-Ampere type equations (Secondary Investigator)
- Parabolic methods for elliptic boundary value problems (Secondary Investigator)
- Variational theory for fully nonlinear elliptic equations (Secondary Investigator)
- Fully nonlinear elliptic equations and applications (Secondary Investigator)
- Nonlinear Elliptic Partial Differential Equations and Applications (Primary Investigator)
- Equations of Monge-Ampere type and applications (Secondary Investigator)
