Abstract
As the title suggests, this is a short presentation of DiBenedetto’s mathematical work. In the first part Ugo Gianazza gives a general overview, without entering too much into details of specific papers; in his contribution Daniele Andreucci focuses on DiBenedetto’s accomplishments in BioMathematics.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
E. DiBenedetto, R.E. Showalter, Implicit degenerate evolution equations and applications. SIAM J. Math. Anal. 12(5), 731–751 (1981)
E. DiBenedetto, Continuity of weak solutions to certain singular parabolic equations. Ann. Mat. Pura Appl. (4) 130, 131–176 (1982)
E. DiBenedetto, V. Vespri, On the singular equation β(u)t = Δu. Arch. Ration. Mech. Anal. 132, 247–309 (1995)
U. Gianazza, B. Stroffolini, V. Vespri, Interior and boundary continuity of the weak solution of the singular equation (β(u))t = Lu. Nonlinear Anal. 56, 157–183 (2004)
U. Gianazza, V. Vespri, Continuity of weak solutions of a singular parabolic equation. Adv. Differ. Equations 8, 1341–1376 (2003)
P. Baroni, T. Kuusi and J.M. Urbano, A quantitative modulus of continuity for the two-phase Stefan problem. Arch. Ration. Mech. Anal. 214, 545–573 (2014)
P. Baroni, T. Kuusi, C. Lindfors, J.M. Urbano, Existence and boundary regularity for degenerate phase transitions. SIAM J. Math. Anal. 50(1), 456–490 (2018)
E. DiBenedetto, Continuity of weak solutions to a general porous medium equation. Indiana Univ. Math. J. 32(1), 83–118 (1983)
E. DeGiorgi, Congetture sulla continuità delle soluzioni di equazioni lineari ellittiche autoaggiunte a coefficienti illimitati, in Typewritten document, Lecce (Italy), January 4 1995 (1995)
E. DeGiorgi, Sulla differenziabilità e l’analiticità delle estremali degli integrali multipli regolari. Mem. Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. (3) 3, 25–43 (1957)
O.A. Ladyzenskaya, N.A. Solonnikov, N.N. Ural’tzeva, Linear and Quasilinear Equations of Parabolic Type. Translations of Mathematical Monographs, vol. 23 (American Mathematical Society, Providence, 1967)
O.A. Ladyzenskaya, N.N. Ural’tzeva, Linear and Quasilinear Elliptic Equations (Academic Press, New York, 1968)
E. DiBenedetto, N. Trudinger, Harnack Inequalities for Quasi-Minima of Variational Integrals. Ann. Inst. Henri Poincaré, Analyse Non Linéaire 1(4), 295–308 (1984)
J. Björn, Sharp exponents and a Wiener type condition for boundary regularity of quasiminimizers. Adv. Math. 301, 804–819 (2016)
E. DiBenedetto, U. Gianazza, A Wiener-type condition for boundary continuity of Quasi-Minima of variational integrals. Manuscripta Math. 149(3–4), 339–346 (2016)
E. DiBenedetto and D.J. Diller, Singular semilinear elliptic equations in \(L^1(\mathbb {R}^N)\), in Topics in Nonlinear Analysis. Program of Nonlinear Differential Equations Application, vol. 35 (Birkhäuser, Basel, 1999), pp. 143–181
E. DiBenedetto, D.J. Diller, About a singular parabolic equation arising in thin film dynamics and in the Ricci flow for complete R 2, in Partial Differential Equations and Applications. Lecture Notes in Pure and Application Mathematics, vol. 177 (Dekker, New York, 1996), pp. 103–119
T. Bhattacharya, E. DiBenedetto, J.J. Manfredi, Limits as p →∞ of Δp u p = f and related extremal problems, in Some Topics in Nonlinear PDEs (Turin, 1989). Rendiconti del Seminario Matematico della Università Politecal, Torino 1989, Special Issue (1991), 15–68
O.D. Kellogg, Foundations of Potential Theory (Dover, New York, 1953)
P. Dive, Attraction des ellipsoïdes homogènes et réciproques d’un théorème de Newton. Bull. Soc. Math. France 59, 128–140 (1931)
E. DiBenedetto, A. Friedman, Bubble growth in porous media. Indiana Univ. Math. J. 35(3), 573–606 (1986)
E. DiBenedetto Classical Mechanics (Cornerstones, Birkhäuser, New York, 2011)
D. Andreucci, P. Bisegna, E. DiBenedetto, Homogenization and concentrated capacity for the heat equation with non–linear variational data in reticular almost disconnected structures and applications to visual transduction. Annali di Matematica Pura e Applicata 182, 375–407 (2003)
D. Andreucci, P. Bisegna, G. Caruso, H. Hamm, E. DiBenedetto, Mathematical model of the Spatio-Temporal dynamics of second messengers in visual transduction. Biophys. J. 85, 1358–1376 (2003)
G. Caruso, H. Khanal, V. Alexiades, F. Rieke, H. Hamm, E. DiBenedetto, Mathematical and computational modelling of spatio-temporal signalling in rod phototransduction. IEE Proc.-Syst. Biol. 152, 119–137 (2005)
G. Caruso, P. Bisegna, L. Shen, D. Andreucci, H. Hamm, E. DiBenedetto, Modeling the Role of Incisures in Vertebrate Phototransduction. Biophys. J. 91, 1192–1212 (2006)
D. Andreucci, P. Bisegna, E. DiBenedetto, Homogenization and concentration of capacity in the rod outer segment with incisures. Appl. Anal. 85, 303–331 (2006)
P. Bisegna, G. Caruso, D. Andreucci, L. Shen, V.V. Gurevich, H. Hamm, E. DiBenedetto, Diffusion of the second messengers in the cytoplasm acts as a variability suppressor of the single photon response in vertebrate phototransduction. Biophys. J. 94, 3363–3383 (2008)
X.-H. Wen, L. Shen, R.S. Brush, N. Michaud, M.R. Al-Ubaidi, V.V. Gurevich, H.E. Hamm, J. Lem, E. DiBenedetto, R.E. Anderson, C.L. Makino, Overexpression of Rhodopsin alters the structure and photoresponse of rod photoreceptors. Biophys. J. 96, 939–950 (2009)
C.L. Makino, X.-H. Wen, N.A. Michaud, H.I. Covington, E. DiBenedetto, H.E. Hamm, J. Lem, G. Caruso, Rhodopsin expression level affects rod outer segment morphology and photoresponse kinetics. PLoSONE 7, e37832 1–7 (2012)
L. Shen, G. Caruso, P. Bisegna, D. Andreucci, V.V. Gurevich, H. Hamm, E. DiBenedetto, Dynamics of mouse rod phototransduction and its sensitivity to variation of key parameters. IET Syst. Biol. 4, 12–32 (2010)
M. Kang, C.A. Day, K. Drake, A.K. Kenworthy, E. DiBenedetto, A generalization of theory for two-dimensional fluorescence recovery after photobleaching applicable to confocal laser scanning microscopes. Biophys. J. 97, 1501–1511 (2009)
M. Kang, C.A. Day, A.K. Kenworthy, E. DiBenedetto, Simplified equation to extract diffusion coefficients from confocal FRAP data. Traffic 13, 1589–1600 (2012)
P. Hinow, C.E. Rogers, C.E. Barbieri, J.A. Pietenpol, A.K. Kenworthy, E. DiBenedetto, The DNA binding activity of p53 displays reaction-diffusion kinetics. Biophys. J. 91, 330–342 (2006)
J.N. McLaughlin, L. Shen, M. Holinstat, J.D. Brooks, E. DiBenedetto, H.E. Hamm, Functional selectivity of G protein signaling by agonist peptides and thrombin for the protease-activated receptor-1. J. Biol. Chem. 280(26), 25048–25059 (2005)
C.J.S. Klaus, K. Raghunathan, E. DiBenedetto, A.K. Kenworthy, Analysis of diffusion in curved surfaces and its application to tubular membranes. Mol. Biol. Cell 27, 3937–3946 (2016)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Andreucci, D., Gianazza, U. (2021). A Short Presentation of Emmanuele’s Work. In: Vespri, V., Gianazza, U., Monticelli, D.D., Punzo, F., Andreucci, D. (eds) Harnack Inequalities and Nonlinear Operators. Springer INdAM Series, vol 46. Springer, Cham. https://doi.org/10.1007/978-3-030-73778-8_2
Download citation
DOI: https://doi.org/10.1007/978-3-030-73778-8_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-73777-1
Online ISBN: 978-3-030-73778-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)