PUBBLICAZIONI

R.Capitanelli, “Nonlinear energy forms on certain fractal curves", J. Nonlinear Convex Anal. 3(2002), no.1, 67--80. 

R.Capitanelli, M.R. Lancia,“Nonlinear energy forms and Lipschitz spaces on the Koch curve",  J.Convex Anal. 9(2002), no.1,245--257. pdf

R.Capitanelli, “Functional inequalities for measure valued Lagrangians on homogeneous spaces ",  Adv.Math. Sci. Appl. 13(2003), no.1, 301--313.

R.Capitanelli, “Homogeneous p-Lagrangians and self-similarity", Rend. Accad. Naz. Sci. XL Mem. Mat. Appl.  27 (2003), 215--235. 

R. Capitanelli, M.R. Lancia,  “Nonlinear energy forms and Lipschitzs spaces on the infinite Koch curve", Special Theme Issue “Wavelet and Fractal Methods in Science and Engineering", Arab. J.Sci. Eng.Sect.C Theme Issues 29 (2004), no. 2, 101--110. 

R.Capitanelli, “Harnack inequalities for p-Laplacians on metric fractals", Progr. Nonlinear Differential Equations Appl., 63 (2005), 119--126. doi:10.1007/3-7643-7384-9_13

R.Capitanelli, “Harnack inequalities for p-Laplacians associated to homogeneous p-Lagrangians",  Nonlinear Analysis Series A: Theory, Methods &Applications 66, no. 6 (2007),1302--1317. doi:10.1016/j.na.2006.01.017.

R.  Capitanelli, “p-Lagrangians on fractals" , Subelliptic PDE's and applications togeometry and finance, Lect. Notes Semin. Interdiscip. Mat. 6(2007), 83--91. 

R.Capitanelli, “Mixed Dirichlet-Robin problems in irregular domains", Journal Communications to SIMAI Congress, VIII Congresso SIMAI. vol. 2(2007) doi:10.1685/CSC06035.

R.Capitanelli, “Richiami di Matematica", In: Rocchi P. “Manuale del Geometra e del Laureato Junior” p.65--123, Proctor  Edizioni, 2009.

R.Capitanelli,  “Transfer across scale  irregular domains",  Series on Advances in Mathematics for Applied Sciences 82 (2009), 165--174 doi: 10.1142/9789814280303_0015 

R.Capitanelli, “Asymptotics for mixed Dirichlet-Robin problems in irregular domains", J. Math. Anal. Appl. 362(2010) ,450--459. doi:10.1016/j.jmaa.2009.09.042.

R.Capitanelli, “Robin boundary condition on scale irregular fractals", Commun.  Pure Appl. Anal. 9 (2010),1221--1234. doi:10.3934/cpaa.2010.9.1221.

R. Capitanelli, M.A. Vivaldi, “Trace Theorems on Scale Irregular Fractals” in “Classification and Application of Fractals”, Nova Publishers, 2011. 

R. Capitanelli, M.A. Vivaldi, “Insulating Layers and Robin Problems on Koch Mixtures”, Journal of Differential Equations 251 (2011),1332-1353. doi:10.1016/j.jde.2011.02.003    

R. Capitanelli, M.A. Vivaldi, “On the Laplacean transfer across fractal mixtures”, Asymptotic Analysis 83 (2013)  (1-2), 1-33. doi:10.3233/ASY-2012-1149

R.Capitanelli, M.R. Lancia, M.A. Vivaldi, “Insulating layers of fractal type”, Differential and Integral Equations 26 (2013) (9-10), 1055-1076. http://projecteuclid.org/euclid.die/1372858561

R. Capitanelli, M.A. Vivaldi, “Uniform weighted estimates on pre-fractal domains”, Discrete Contin. Dyn. Syst. Ser B 19 (2014), no. 7, 1969-1985. doi:10.3934/dcdsb.2014.19.1969

R. Capitanelli, M.A. Vivaldi, “Weighted estimates on fractal domains”,  Mathematika,  61 (2015),  no. 2, 370 —384. DOI:http://dx.doi.org/10.1112/S0025579314000400

R. Capitanelli, M.A. Vivaldi, “Quasi-filling fractal layers”, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl.  26  (2015), no.4, 465-473, doi:10.4171/RLM/716

R. Capitanelli, M.A. Vivaldi, “Reinforcement problems  for variational inequalities on fractal sets”, Calculus of Variations and Partial Differential Equations 54 (2015), no.3, 2751-2783. doi:10.1007/s00526-015-0882-6. 

F. Camilli,  R. Capitanelli, C. Marchi, “ Eikonal equations on the Sierpinski gasket”, Mathematische Annalen 364 (2016), no 3, 1167 - 1188 doi:10.1007/s00208-015-1251-7. 

R. Capitanelli, M.A. Vivaldi, “ Dynamical Quasi-Filling Fractal Layers". SIAM J. Math. Anal.48 (2016), no. 6, 3931–3961.

 http://dx.doi.org/10.1137/15M1043893

R. Capitanelli, M D'Ovidio, "Asymptotic for time-changed diffusion",  Probability Theory and Mathematical Statistics  (2016), no. 95,

37-54 http://probability.univ.kiev.ua/tims/index.php?year=2016&volume=95

R. Capitanelli, M D'Ovidio, "Skew Brownian diffusions across Koch interfaces", Potential analysis 46 (2017), no. 3, 431–461. doi: http://dx.doi.org/10.1007/s11118-016-9588-4

F. Camilli,  R. Capitanelli, M.A. Vivaldi, "Absolutely Minimizing Lipschitz Extensions and infinity harmonic functions on the Sierpinski gasket", Nonlinear Anal. 163 (2017), 71–85. https://doi.org/10.1016/j.na.2017.07.005

R. Capitanelli, C. Pocci, "On the effective interfacial resistance through quasi-filling fractal layers", Chaos, Solitons & Fractals

105  (2017),  43-50.   https://doi.org/10.1016/j.chaos.2017.09.036 

R. Capitanelli, M.A. Vivaldi, “FEM for quasilinear obstacle problems in bad domains", ESAIM: M2AN 51 (2017), 6, 2465-2485 https://doi.org/10.1051/m2an/2017033

R. Capitanelli, C. Pocci,  “Periodic homogenization for quasi-filling fractal layers",  Communications in Contemporary Mathematics 20 (2018), no.8, 1750088-1 - 1750088-26       https://doi.org/10.1142/S0219199717500882

R. Capitanelli,  S. Fragapane, M. A. Vivaldi, "Regularity results for p-Laplacian in pre-fractal domains", Advances

 in Nonlinear Analysis  8 (2019), no. 1, 1043–1056. https://doi.org/10.1515/anona-2017-0248

R. Capitanelli, S. Fragapane, "Asymptotics for quasilinear obstacle problems in bad domains", Discrete and Continuous Dynamical Systems - Series S 12 (2019), no.1, 43-56.  http://aimsciences.org/article/doi/10.3934/dcdss.2019003

R. Capitanelli, M. D'Ovidio," Fractional equations via convergence of forms". Fract. Calc. Appl. Anal. 22 (2019), no. 4, 844–870.  https://doi.org/10.1515/fca-2019-0047

R. Capitanelli, M. D'Ovidio," Delayed and rushed motions through time change", ALEA, Lat. Am. J. Probab. Math. Stat. 17, 183–204 (2020)  http://alea.impa.br/articles/v17/17-08.pdf

R. Capitanelli, M.A. Vivaldi, “Sharp Trudinger Type Inequalities for Measure-Valued Lagrangeans",  Journal of Convex Analysis 28 (2021), No. 2, [final page numbers not yet available] http://www.heldermann.de/JCA/JCA28/JCA282/jca28025.htm

R. Capitanelli, M. D'Ovidio, "Fractional Cauchy problem on random snowflakes", Journal of Evolution Equations  21 (2021), 2123--2140    DOI 10.1007/s00028-021-00673-7   https://rdcu.be/cfEXh

C. Alberini, R. Capitanelli, S. F. Finzi Vita, "A numerical study of a degenerate diffusion equation driven by a Heaviside function",  Computers and Mathematics with Applications, 89 (2021). 139-149 https://doi.org/10.1016/j.camwa.2021.03.002

 R. Capitanelli, M. D'Ovidio, " Approximation of space-time fractional equations",  Fractal and Fractional 5 (2021),  71.

R. Capitanelli, M.A. Vivaldi, “Limit of 𝑝-Laplacian obstacle problems", Advances in Calculus of Variations, Advances in Calculus of Variations 15 (2022) no. 2, 265--286. https://doi.org/10.1515/acv-2019-0058

C. Alberini, R. Capitanelli,  M. D'Ovidio, S. Finzi Vita,  "On the time fractional heat equation with obstacle",  Journal of Computational and Applied Mathematics, 415 (2022), Paper No. 114470, 11 pp. https://doi.org/10.1016/j.cam.2022.114470

R. Capitanelli, S. Creo,  M. R. Lancia,  "Asymptotics for time-fractional Venttsel' problems in fractal domains",  Fractal Fract. 2023, 7(6), 479; https://doi.org/10.3390/fractalfract7060479

R. Capitanelli,  "Time fractional equations on Sierpinski gasket like fractals" to appear on  AMS Contemporary Mathematics.

PREPRINT

R. Capitanelli, S. Fragapane “Convergence results for the solutions of (p,q)-Laplacian double obstacle problems on irregular domains”

Other publications

R. Capitanelli, “Richiami di Matematica”, In: Rocchi P. “Manuale del Geometra e del Laureato Junior” p. 65–123, Proctor Edizioni, 2009.

S. Camiz, D. Capecchi, R. Capitanelli, “Quale Matematica per l’Architettura?”, DISG Library, 2014 ISBN: 9781291923063

A.M. Bersani, R. Capitanelli, E. N. M Cirillo, C. Ricciuti, B. Vantaggi “Il fascino della matematica e delle sue applicazioni”, CompoMat S.r.l. ISBN: 978-88-95706-54-2

R. Capitanelli, “Lagrangians on homogenous spaces”, Advisor Prof. U. Mosco, Phd Thesis  in Matematics, Università degli Studi di Roma “La Sapienza”, 2001.