Publications

 

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

More information at Rolando Magnanini on Researchgate

Papers on Journals

  1. Nonlinear asymptotic mean value characterization of holomorphic functions, (with R. Durastanti), preprint (2023) arxiv:2306.08437.

  2. The interior Backus problem: local resolution in Holder spaces, (with T. Kan and M. Onodera), to appear in J. Differential Eqs., preprint (2022) arxiv:2212.00413.

  3. Quantitative symmetry in a mixed Serrin-type problem for a constrained torsional rigidity, (with G. Poggesi), preprint (2022) arxiv:2210.10288.

  4. Explicit complex-valued solutions of the 2D eikonal equation, Appl. Anal. 101, n. 11 (2022), 3934-3946 (Special Issue in honour of R. Gilbert's Ninetieth Birthday), doi: 10.1080/00036811.2022.2036726, preprint (2021) arxiv:2111.10852

  5. Interpolating estimates with applications to some quantitative symmetry results, (with G. Poggesi), Mathematics in Engineering 2023, Volume 5, Issue 1: 1-21. doi: 10.3934/mine.2023002, preprint (2021) arxiv:2109.02876.

  6. Backus problem in geophysics: a resolution near the dipole in fractional Sobolev spaces, (with T. Kan, M. Onodera), Nonlinear Differ. Equ. Appl. (NoDEA) 29 (2022), Paper n. 21, 29 pp. doi: 10.1007/s00030-022-00749-4, preprint (2021) arxiv:2108.12077.

  7. Variational p-harmonious functions: existence and convergence to p-harmonic functions, (with E. W. Chandra, M. Ishiwata, H. Wadade), Nonlinear Differ. Equ. Appl. (NoDEA) 28 (2021). Paper n. 51, 23 pp. doi.org/10.1007/s00030-021-00714-7, preprint (2021) arxiv:2101.02662.

  8. The location of hot spots and other extremal points, (with G. Poggesi), Math. Ann. 384 (2022), pp. 1-39 Springer Sharedit, Math. Ann. Springer link doi.org/10.1007/s00208-021-02290-8, preprint (2020) arxiv:2005.13175.

  9. An interpolating inequality for solutions of uniformly elliptic equations, (with G. Poggesi), in Geometric Properties for Parabolic and Elliptic PDEs, Springer INdAM Series vol. 47, pp. 233-245. V. Ferone, T. Kawakami, P. Salani, F. Takahashi Eds. Springer Verlag 2021. Preprint submitted (2020) arxiv:2002.04332.

  10. Small diffusion and short time asymptotics for Pucci's operators, (with D. Berti), Appl. Anal. 101, n. 10 (2022), 3716-3732 , published online in Applicable Analysis DOI:1080/00036811.2020.1750602, preprint (2020) arxiv:2001.01112.

  11. Nearly optimal stability for Serrin's problem and the Soap Bubble Theorem, (with G. Poggesi), Calc. Var. 59 (2020). Paper n. 35, 23 pp. doi.org/10.1007/s00526-019-1689-7, preprint (2019) arxiv:1903.04823.

  12. Asymptotics for the resolvent equation associated to the game-theoretic p-laplacian, (with D. Berti), Appl. Anal. 98 (2019), 1827-1842, preprint (2018) arxiv:1801.04230.

  13. Two-phase heat conductors with a surface of the constant flow property, (with L. Cavallina and S. Sakaguchi), J. Geom. Anal. 31 (2021), 312-345. Appeared online in J. Geom. Anal., DOI: 10.1007/s112220-019-00262-8, preprint (2018) arxiv:1801.01352.

  14. Short-time behavior for game-theoretic p-caloric functions, (with D. Berti), Jour. Math. Pures Appl. 126 (2019), 249-272, preprint (2017) arxiv:1709.10005.

  15. Alexandrov, Serrin, Weinberger, Reilly: symmetry and stability by integral identities, Bruno Pini Mathematical Seminar (2017), 121-141, preprint (2017) arxiv:1709.073939.

  16. Serrin's problem and Alexandrov's Soap Bubble Theorem: enhanced stability via integral identities, (with G. Poggesi), Indiana Univ. Math. Jour. 69 (2020), no. 4, 1181-1205, preprint (2017) arxiv:1708.07392.

  17. On the stability for Alexandrov's Soap Bubble Theorem, (with Giorgio Poggesi), Jour. Anal. Math. 139 (2019), 179-205 online DOI: 10.1007/s111854-019-0058-y , preprint (2016) (arxiv:1610.07036).

  18. An introduction to the study of critical points of solutions of elliptic and parabolic equations, Rend. Istit. Mat. Univ. Trieste 48 (2016), 121-166 ( RIMUT2016).

  19. A natural approach to the asymptotic mean value property for the p-Laplacian, (with Michinori Ishiwata and Hidemitsu Wadade), Calc. Var. Part. Diff. Eqs. 56 (2017), 56-97, preprint arxiv (2016) (arxiv:1604.00520).

  20. Symmetry and linear stability in Serrin's overdetermined problem via the stability of the parallel surface problem, (with G. Ciraolo and V. Vespri) preprint (2015) (arxiv:1505.07531).

  21. The Matzoh Ball Soup problem: a complete characterization, (with M. Marini), Nonlinear Anal. 131 (2016), 170-181 (arxiv:1505.02638).

  22. Hölder stability for Serrin's overdetermined problem, (with G. Ciraolo and V. Vespri), Ann. Mat. Pura Appl. 195 (2016), 1333-1345 (DOI:10.1007/s10231-015-0518-7) (arxiv:1410.7791).

  23. Stationary isothermic surfaces in Euclidean 3-space (with D. Peralta-Salas and S. Sakaguchi), Math. Ann. 364 (2016), 97-124. DOI:10.1007/s00208-015-1212-1.

  24. Littlewood's fourth principle, (with. G. Poggesi) Springer Proc. Math. Stat. 176 (2016), 149-158 (arxiv:1408.0920).

  25. A note on Serrin's overdetermined problem, (with G. Ciraolo) Kodai Math. Jour. 37 (2014), 728-736 (arxiv:1401.4385).

  26. Characterization of ellipsoids as K-dense sets, (with M. Marini), Proc. Roy. Soc. Edin. 146 (2016), 213-223 (arxiv:1308.0817).

  27. Solutions of elliptic equations with a level surface parallel to the boundary:stability of the radial configuration, (with G. Ciraolo e S. Sakaguchi) J. Anal. Math. 128 (2016), 337-353 arxiv:1307.1257) DOI 10.1007/s11854-016-0011-2.

  28. Characterization of ellipses as uniformly dense sets with respect to a family of convex bodies, (with M. Marini) Ann. Mat. Pura Appl. 193 (2014), 1383-1395, available online SpringerLink (also at arxiv:1206.4238 or eprints.unifi.it).

  29. Symmetry of minimizers with a level surface parallel to the boundary, (with G. Ciraolo and S. Sakaguchi) J. Eur. Math. Soc. (JEMS) 17 (2015), 2789-2804. (arxiv:1203.5295v1 or eprints.unifi.it).

  30. The heart of a convex body, (with L. Brasco) in "Geometric Properties of Parabolic and Elliptic PDE's", Springer INdAM Series , R. Magnanini, S. Sakaguchi and A. Alvino Eds., Springer Verlag 2012. DOI:10.1007/978-88-470-2841-8_4. (arxiv:1202.5223v1 or eprints.unifi.it). 

  31. Matzoh ball soup revisited: the boundary regularity issue, (with S. Sakaguchi) Math. Meth. Appl. Sci. 36 (2013), 2023-2032, first published online on June 18, 2012, DOI: 10.1002/mma.1551. (arxiv:1103.6229 or eprints.unifi.it). 

  32. The location of the hot spot in a grounded convex conductor, (with L. Brasco and P. Salani) Indiana University Mathematical Journal 60 (2011), 633-660. (arXiv:1012.4742 or eprints.unifi.it). 

  33. Interaction between nonlinear diffusion and geometry of domain. (with S. Sakaguchi) J. Differential Eqs. 252 (2012), 236-257. (arXiv:1009.6131 ). 

  34. Stability in an overdetermined problem for the Green's function, (with V. Agostiniani) Ann. Mat. Pura Appl. 190 (2011), 21-31. (arXiv:1001.1544v1). 

  35. Preface to "Geometric Properties of Parabolic and Elliptic PDE's", (with F. Gazzola and S. Sakaguci) Discrete and Continuous Dynamical Systems, Series S, 4 (2011), I-II (unload article.pdf ). 

  36. Symmetries in an overdetermined problem for the Green's function, (with V. Agostiniani) Discrete and Continuous Dynamical Systems, Series S, 4 (2011), 791-800. (unload article.pdf). 

  37. On complex-valued 2D eikonals. Part four: continuation past a caustic, (with G. Talenti), Milan Journal of Mathematics 77 no. 1 (2009), 1-66; DOI:10.1007/s00032-009-0103-x. (unload article.pdf) 

  38. Nonlinear diffusion with a bounded stationary level surface, (with S. Sakaguchi) Ann. Inst. Henri Poincaré Analyse Nonliné aire 27 (2010), 937-952. (arXiv:0902.1929) 

  39. Critical points of solutions of degenerate elliptic equations in the plane, (with S. Cecchini) Calculus of Variations and PDE's 39 (2010), 121-138. (unload article.pdf) 

  40. Stationary isothermic surfaces and some characterizations of the hyperplane in the N-dimensional Euclidean space, (with S. Sakaguchi) J. Differential Eqs. 248 (2010), 1112-1119. (arXiv:0812.2165) 

  41. 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. 

  42. Stationary isothermic surfaces for unbounded domains, (with S. Sakaguchi) Indiana Univ. Math. Journ. 56, no. 6 (2007), 2723-2738. (unload article.pdf) 

  43. Polygonal heat conductors with a stationary hot spot, (with S. Sakaguchi) J. d'Anal. Math. 105 (2008), 1-18. (unload article.pdf) 

  44. 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) 

  45. 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) 

  46. Interaction between degenerate diffusion and shape of domain, (with S. Sakaguchi) Proc. Royal Soc. Edinburgh 137A (2007), 373-388. (unload article.pdf) 

  47. 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) 

  48. Stationary isothermic surfaces and uniformly dense domains, (with J. Prajapat and S. Sakaguchi) Trans. A.M.S. 385 (2006), 4821-4841. (unload article.pdf) 

  49. 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 ) 

  50. 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 ) 

  51. 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) 

  52. Matzoh ball soup: heat conductors with a stationary isothermic surface, (with S. Sakaguchi) Annals of Mathematics 156 (2002), 941-956. (unload article.ps) 

  53. 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 ) 

  54. Stationary critical points of the heat flow in the plane, (with S. Sakaguchi), J. d'Anal. Math. 88 (2002), 383-396. (unload article.ps ) 

  55. 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) 

  56. 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) 

  57. 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) 

  58. 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) 

  59. 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) 

  60. 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) 

  61. 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) 

  62. 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) 

  63. 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) 

  64. 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. 

  65. 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). 

  66. On symmetric invariants of level surfaces near regular points, Journ. London Math. Soc. 24 (1992), 565-574, London. 

  67. On functions whose curves of steepest descent are straight lines, Applicable Analysis 41 (1991), 171-182, London. 

  68. A fully nonlinear boundary value problem for the Laplace equation in dimension two, Applicable Analysis 39(1990), 185-192, London. 

  69. 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). 

  70. 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. 

  71. 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). 

  72. The boundary integral method for two-dimensional orthotropic plates, (with R.P. Gilbert) Journal of Elasticity 18 (1987), 61-82, Dordrecht (NL). 

  73. On a (new) nonlinear boundary value problem for the Laplace equation, Technical Report 86-7, University of Delaware. 

  74. An inverse problem for the Helmholtz equation, (with G. Papi) Inverse Problems 1 (1985), 357-370, Bristol (GB). published article  

  75. Sulla lipschitzianità delle soluzioni di equazioni ellittiche a coefficienti radiali, Le Matematiche XXXV (1980), 311-324, Catania. 

  76. Una osservazione sulla continuità delle soluzioni di equazioni ellittiche, Boll. UMI (5) 18-A (1981), 477-482, Bologna. 

    Books and Proceedings Edited

  77. Chapter V. 9 Geometric properties of solutions of PDE's. Progress in Analysis, H.G.W. Begehr, R.P. Gilbert, M.W. Wong Eds. World Scientific, New Jersey, 2003, 861-896.

  78. 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).

  79. Geometric Properties of Parabolic and Elliptic PDE's, (with F. Gazzola and S. Sakaguci) Discrete and Continuous Dynamical Systems, Series S, 4 (2011), I-II.

  80. Geometric Properties of Parabolic and Elliptic PDE's. Springer INdAM Series, R. Magnanini, S. Sakaguchi and A. Alvino Eds., Springer Verlag 2012. DOI:10.1007/978-88-470-2841-8_4 

  81. Geometry of PDEs and Related Problems, Lecture Notes in Mathematics Vol. 2220, CIME Foundation Subseries, C. Bianchini, A. Henrot, R. Magnanini Eds., (2018), 190 pp., 32 illus., 4 illus. in color Springer Verlag ISBN 978-3-319-95186-7.

  82. Geometric and regularity properties of solutions to elliptic and parabolic PDEs, L. Brasco, R. Magnanini, P. Bousquet Eds., in Current Trends in Analysis, its Applications and Computation, Proceedings of the 12th ISAAC Congress, Aveiro, Portugal 2019. P. Cerejeiras, M. Reissig, I. Sabadini, J. Toft Eds., Birkhauser 2022.



     
     
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