Publications

 

Below is a list of my publications. The titles that cannot be unloaded can be requested by sending me an e-mail at the address: magnanin@math.unifi.it.

  1. Una osservazione sulla continuità delle soluzioni di equazioni ellittiche, Boll. UMI (5) 18-A (1981), 477-482, Bologna.
  2. Sulla lipschitzianità delle soluzioni di equazioni ellittiche a coefficienti radiali, Le Matematiche XXXV (1980), 311-324, Catania.
  3. An inverse problem for the Helmholtz equation, (with G. Papi) Inverse Problems 1 (1985), 357-370, Bristol (GB).
  4. On a (new) nonlinear boundary value problem for the Laplace equation, Technical Report 86-7, University of Delaware.
  5. The boundary integral method for two-dimensional orthotropic plates, (with R.P. Gilbert) Journal of Elasticity 18 (1987), 61-82, Dordrecht (NL).
  6. A moving boundary problem associated with flow through a porous medium, (with R.P. Gilbert) Nonlinear Analysis, Theory, Methods & Applications 12 (1988), 109-119, Oxford (GB).
  7. A fully nonlinear boundary value problem for the Laplace equation, Proc. VII Intern. Conf. on Nonlinear Analysis and Applications. Ed. V. Lakshmikantham. Lecture Notes in Pure and Applied Mathematics 109. Marcel Dekker, New York 1987.
  8. Pure bending problem for a vibrating elastic plate with non-uniform temperature, (with J. Buchanan-R.P. Gilbert) Journal of Elasticity 20 (1988), 93- 112, Dordrecht (NL).
  9. A fully nonlinear boundary value problem for the Laplace equation in dimension two, Applicable Analysis 39(1990), 185-192, London.
  10. On functions whose curves of steepest descent are straight lines, Applicable Analysis 41 (1991), 171-182, London.
  11. On symmetric invariants of level surfaces near regular points, Journ. London Math. Soc. 24 (1992), 565-574, London.
  12. Explicit calculation of the solution to Backus' problem with a condition for uniqueness,(with M.C. Jorge) J. Math. Anal. Appl. 173 (1993), 515-522, Orlando, FL. (USA).
  13. The index of isolated critical points and solutions of elliptic equations in the plane, (with G. Alessandrini) Ann. Scuola Norm. Sup. Pisa Cl. Sc. 19 (4) (1992), 567-589.
  14. Symmetry and non-symmetry for the overdetermined Stekloff eigenvalue problem, (with G. Alessandrini) Journ. Appl. Math. Phys. (ZAMP) 45 (1994), 44-52. (unload article.pdf)
  15. Elliptic equations in divergence form, geometric critical points of solutions, and Stekloff eigenfunctions, (with G. Alessandrini) SIAM J. Math. Anal. 25 (1994), 1259-1268. (unload article.pdf)
  16. Symmetry and non-symmetry for the overdetermined Stekloff eigenvalue problem II, (with G. Alessandrini) in Nonlinear Problems in Applied Mathematics, L. P. Cook et al. eds., SIAM, Philadelphia 1995. (unload article.pdf)
  17. The spatial critical points not moving along the heat flow, (with S. Sakaguchi) J. d'Anal. Math. 71 (1997), 237-261. (unload article.ps) and (view abstract.pdf)
  18. The spatial critical points not moving along the heat flow II: The centrosymmetric case, (with S. Sakaguchi) Math. Z. 230 (1999), 695-712. (unload article.ps) , (errata) and (view abstract.pdf)
  19. On complex-valued solutions to a 2D eikonal equation. Part one: qualitative properties, (with G. Talenti) in Nonlinear Partial Differential Equations, Gui-Qiang Chen e Emmanuele Di Benedetto eds., Contemporary Mathematics, American Mathematical Society 1999. (unload article) and (view abstract.pdf)
  20. Wave propagation in a 2-D optical waveguide, (with F. Santosa,) SIAM Journ. on Applied Anal. 61 (2000), 1237-1252, Philadelphia (USA). (unload article.ps ) and (view abstract.pdf)
  21. Scattering in a 2-D optical waveguide, (with F. Santosa,) in Analytical and Computational Methods in Scattering and Applied Mathematics, F. Santosa ed I. Stakgold eds., CRC Press, London 1999. (unload article.ps) and (view abstract.pdf)
  22. On complex-valued solutions to a 2D eikonal equation. Part two: existence theorems, (with G. Talenti) SIAM J. Math. Anal. 34 (2003), 805-835. (unload article) and (view abstract.pdf)
  23. Stationary critical points of the heat flow in the plane, (with S. Sakaguchi), J. d'Anal. Math. 88 (2002), 383-396. ( unload article.ps )
  24. On heat conductors with a stationary hot spot, (with S. Sakaguchi) Annali Matematica Pura ed Applicata 183, no. 1 (2004), 1-23. ( unload article.ps )
  25. Matzoh ball soup: heat conductors with a stationary isothermic surface, (with S. Sakaguchi) Annals of Mathematics 156 (2002), 941-956. ( unload article.ps)
  26. Approaching a partial differential equation of mixed elliptic-hyperbolic type, (with G. Talenti) in Ill-posed and Inverse Problems, V.G. Romanov, S.I. Kabanikhin, Yu.E. Anikonov, A.L. Bukhgeim eds., VSP 2002, pp. 263-276. (unload article) (view abstract.pdf)
  27. On stationary hot spots and isothermic surfaces, in Progress in Analysis, Proceedings of the Third International ISAAC Congress, Berlin (Germany), H.G.W. Begehr et al. eds., World Scientific, New Jersey, 2003. ( unload article.ps )
  28. On isophonic surfaces, in Acoustics, Mechanics and the Related Topics of Mathematical Analysis, Proceedings of the International Conference to Celebrate Robert P. Gilbert's 70th Birthday. Ed. A. Wirgin, World Scientific, New Jersey 2002. ( unload article.ps )
  29. Stationary isothermic surfaces and uniformly dense domains, (with J. Prajapat and S. Sakaguchi) Trans. A.M.S. 385 (2006), 4821-4841. ( unload article.pdf)
  30. On complex-valued solutions to a 2D Eikonal Equation. Part Three: analysis of a Backlund transformation, (with G. Talenti) Applic. Anal. 85, no. 1-3 (2006), 249-276. ( unload article.ps)
  31. Special Issue of Applicable Analysis in Memory of Carlo Pucci R.P. Gilbert, R. Magnanini and G. Talenti Eds. Applic. Anal. 85, no. 1-3 (2006).
  32. Interaction between degenerate diffusion and shape of domain, (with S. Sakaguchi) Proc. Royal Soc. Edinburgh 137A (2007), 373-388. ( unload article.pdf)
  33. On the curvature of free boundaries with a Bernoulli-type condition, (with S. Cecchini) Nonlinear Analysis, Theory Methods and Applications 68 (2008), 940-950. ( unload article.pdf)
  34. Analytical results for 2-D non-rectilinear waveguides based on the Green's function, (with G. Ciraolo) Math. Meth. Appl. Sci. 31 (2008), 1587-1606. ( unload article.pdf)
  35. Polygonal heat conductors with a stationary hot spot, (with S. Sakaguchi) J. d'Anal. Math. 105 (2008), 1-18. ( unload article.pdf)
  36. Stationary isothermic surfaces for unbounded domains, (with S. Sakaguchi) Indiana Univ. Math. Journ. 56, no. 6 (2007), 2723-2738. ( unload article.pdf)
  37. A radiation condition for uniqueness in a wave propagation problem for 2-D open waveguides, (with G. Ciraolo) Math. Meth. Appl. Sci. 32 (2009), 1183-1206.
  38. Stationary isothermic surfaces and some characterizations of the hyperplane in the N-dimensional Euclidean space, (with S. Sakaguchi) preprint (2008) ( arXiv:0812.2165)
  39. Critical points of solutions of degenerate elliptic equations in the plane, (with S. Cecchini) to appear on Calculus of Variations and PDE's (2009) ( arXiv:0812.4244)
  40. Nonlinear diffusion with a bounded stationary level surface, (with S. Sakaguchi) preprint (2009) ( arXiv:0902.1929)
  41. On complex-valued 2D eikonals. Part four: continuation past a caustic, (with G. Talenti), Milan Journal of Mathematics DOI:10.1007/s00032-009-0103-x. ( arxiv:0905.2690)
  42. Symmetries in an overdetermined problem for the Green's function, (with V. Agostiniani) preprint (2009) ( ).

    43.  

     

    Teaching                            Research                             Links