T. Allen and C. Arkolakis, Trade and the Topography of the Spatial Economy *, The Quarterly Journal of Economics, vol.311, issue.3, pp.1085-1139, 2014.
DOI : 10.1016/j.jmaa.2005.03.084

A. Aslund and M. Dabrowski, Challenges of globalization: Imbalances and growth. Peter G. Peterson for International Economics, 2008.

R. Barro and X. Sala-i-martin, Economic Growth, 1995.
DOI : 10.1007/978-1-349-27904-3_14

R. B. Barsky, F. T. Juster, M. S. Kimball, and M. D. Shapiro, Preference Parameters and Behavioral Heterogeneity: An Experimental Approach in the Health and Retirement Study, The Quarterly Journal of Economics, vol.1, issue.2, pp.537-579, 1997.
DOI : 10.2307/2937817

A. Birkisson and T. A. Driscoll, Automatic Fr??chet Differentiation for the Numerical Solution of Boundary-Value Problems, ACM Transactions on Mathematical Software, vol.38, issue.4, pp.1-26, 2012.
DOI : 10.1145/2331130.2331134

R. Boucekkine, G. Fabbri, and F. Gozzi, Egalitarianism under population change: Age structure does matter, Journal of Mathematical Economics, vol.55, pp.86-100, 2014.
DOI : 10.1016/j.jmateco.2014.10.007
URL : https://hal.archives-ouvertes.fr/hal-01463923

R. Boucekkine, C. Camacho, and G. Fabbri, Spatial dynamics and convergence: The spatial AK model, Journal of Economic Theory, vol.148, issue.6, pp.2719-2736, 2013.
DOI : 10.1016/j.jet.2013.09.013
URL : https://hal.archives-ouvertes.fr/hal-00973387

R. Boucekkine, C. Camacho, and B. Zou, BRIDGING THE GAP BETWEEN GROWTH THEORY AND THE NEW ECONOMIC GEOGRAPHY: THE SPATIAL RAMSEY MODEL, Macroeconomic Dynamics, vol.13, issue.01, pp.20-45, 2009.
DOI : 10.1016/S0362-546X(98)00258-2
URL : https://hal.archives-ouvertes.fr/hal-00683809

R. Boucekkine, D. De-la-croix, and D. Peeters, Early Literacy Achievements, Population Density, and the Transition to Modern Growth, Journal of the European Economic Association, vol.69, issue.2, pp.183-226, 2007.
DOI : 10.1016/j.eeh.2003.09.001

H. Brezis, Functional Analysis, Sobolev Sapces and Partial Differential Equations, 2011.

P. Brito, The dynamics of growth and distribution in a spatially heterogeneous world Working Papers Department of Economics, 2004.

W. Brock and A. Xepapadeas, Diffusion-induced instability and pattern formation in infinite horizon recursive optimal control, Journal of Economic Dynamics and Control, vol.32, issue.9, pp.2745-2787, 2008.
DOI : 10.1016/j.jedc.2007.08.005

B. M. Brown, M. S. Eastham, and K. M. Shmidt, Periodic Differential Operators, Operator Theory, Advances and Applications, vol.230, 2013.
DOI : 10.1007/978-3-0348-0528-5

A. Ciccone and R. E. Hall, Productivity and the density of economic activity, The American Economic Review, vol.86, issue.1, pp.54-70, 1996.
DOI : 10.3386/w4313

D. A. Comin, M. Dmitriev, and E. Rossi-hansberg, The spatial diffusion of technology, National Bureau of Economic Research, 2012.
DOI : 10.3386/w18534

K. Desmet and E. Rossi-hansberg, ON SPATIAL DYNAMICS, Journal of Regional Science, vol.74, issue.1, pp.43-63, 2010.
DOI : 10.1017/CBO9780511805660.011

T. A. Driscoll, H. , and N. , Rectangular spectral collocation, IMA Journal of Numerical Analysis, vol.17, issue.1, pp.108-132, 2016.
DOI : 10.1137/0725072

G. Fabbri, Geographical structure and convergence: A note on geometry in spatial growth models, Journal of Economic Theory, vol.162, issue.1, pp.114-136, 2016.
DOI : 10.1016/j.jet.2015.12.004
URL : https://hal.archives-ouvertes.fr/hal-01446208

G. Fabbri, F. Gozzi, and A. Swiech, Stochastic Optimal control in Infinite Dimension . Dynamic Programming and HJB Equations, Series in Probability Theory and Stochastic Modeling, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01447562

H. O. Fattorini, Infinite Dimensional Optimization and Control Theory, 1999.
DOI : 10.1017/CBO9780511574795

M. Fujita and J. Thisse, Economics of agglomeration: Cities, industrial location, and regional growth, 2002.
DOI : 10.1017/CBO9780511805660

O. Galor and D. Weil, Population, Technology, and Growth: From Malthusian Stagnation to the Demographic Transition and Beyond, American Economic Review, vol.90, issue.4, pp.806-828, 2000.
DOI : 10.1257/aer.90.4.806

W. Isard and P. Liossatos, Spatial Dynamics and Optimal Space-time Development, 1979.

P. Krugman, FIRST NATURE, SECOND NATURE, AND METROPOLITAN LOCATION, Journal of Regional Science, vol.64, issue.2, pp.129-144, 1993.
DOI : 10.1086/261763

P. Krugman, Increasing Returns and Economic Geography, Journal of Political Economy, vol.99, issue.3, pp.483-499, 1991.
DOI : 10.1086/261763
URL : http://www.princeton.edu/pr/pictures/g-k/krugman/krugman-increasing_returns_1991.pdf

D. Levhari, Y. Oron, and D. Pibes, A note on unequal treatment of equals in an urban setting, Journal of Urban Economics, vol.5, issue.2, pp.278-284, 1978.
DOI : 10.1016/0094-1190(78)90029-3

H. Lopez, The social discount rate : estimates for nine Latin American countries. The World Bank Policy Research Working Paper Series 4639, 2008.

P. Martin, R. , and C. A. , Industrial location and public infrastructure, Journal of International Economics, vol.39, issue.3-4, pp.335-351, 1995.
DOI : 10.1016/0022-1996(95)01376-6

E. Mills and M. , Notes on the New Urban Economics, The Bell Journal of Economics and Management Science, vol.4, issue.2, pp.593-601, 1973.
DOI : 10.2307/3003054

J. Mirrlees, The optimum town, Swedish Journal of Economics, vol.74, pp.115-135, 1972.
DOI : 10.2307/3439013

P. Mossay, Increasing returns and heterogeneity in a spatial economy, Regional Science and Urban Economics, vol.33, issue.4, pp.419-444, 2003.
DOI : 10.1016/S0166-0462(02)00041-8

P. Nijkamp and J. Poot, Spatial perspectives on new theories of economic growth. The annals of regional science, pp.7-37, 1998.

K. Petersen, Ergodic Theory, 1983.
DOI : 10.1017/CBO9780511608728

T. Piketty and G. Zucman, Capital is Back: Wealth-Income Ratios in Rich Countries 1700???2010 *, The Quarterly Journal of Economics, vol.128, issue.4, pp.1255-1310, 2014.
DOI : 10.1093/qje/qjt012
URL : https://hal.archives-ouvertes.fr/halshs-01109372

D. Wildasin, Spatial variation of the marginal utility of income and unequal treatment of equals, Journal of Urban Economics, vol.19, issue.1, pp.125-129, 1986.
DOI : 10.1016/0094-1190(86)90034-3

. World-bank and . Group, World Development Indicators 2016, 2016.
DOI : 10.1596/978-1-4648-0683-4

R. Boucekkine, CNRS and EHESS. 2, Place Le Verrier E-mail address: raouf.boucekkine@univ-amu.fr G. Fabbri E-mail address: giorgio.fabbri@univ-grenoble-alpes.fr S. Federico