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1. Lipschitz continuity results for a class of obstacle problems

Author

Benassi, Carlo and Caselli, Michele

Subjects
Mathematics - Analysis of PDEs, 35B65
Abstract

We prove Lipschitz continuity results for solutions to a class of obstacle problems under standard growth conditions of $p$-type, $p \geq 2$. The main novelty is the use of a linearization technique going back to [28] in order to interpret our constrained minimizer as a solution to a nonlinear elliptic equation, with a bounded right-hand side. This leads us to start a Moser iteration scheme which provides the $L^\infty$ bound for the gradient. The application of a recent higher differentiability result [24] allows us to simplify the procedure of the identification of the Radon measure in the linearization technique employed in [32]. To our knowledge, this is the first result for non-autonomous functionals with standard growth conditions in the direction of the Lipschitz regularity.

Published
2022
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2. The Fundamental Theorem of Integral Calculus: a Volterra's generalization applied to flat functions

Author

Benassi, Carlo and Eleuteri, Michela

Subjects
Mathematics - History and Overview, Mathematics - Classical Analysis and ODEs
Abstract

In a recent paper [5] a smooth function f : [0; 1] --> R with all derivatives vanishing at 0 has been considered and a global condition, showing that f is indeed identically 0, has been presented. The purpose of this note is to replace the classical Fundamental Theorem of Calculus for the Riemann integral, as it has been used in [5], with a weaker form going back to Volterra [7], which is little known. Therefore the proof we propose in this paper turns to be important also from the teaching point of view, as long as in literature there are very few examples in which explicitly the lower integral and the upper integral of a function appear (usually the assumption that the function is Riemann-integrable is required).

Published
2020

3. Covariogram of non-convex sets

Author

Benassi, Carlo, Bianchi, Gabriele, and D'Ercole, Giuliana

Subjects
Mathematics - Metric Geometry
Abstract

The covariogram of a compact set A contained in R^n is the function that to each x in R^n associates the volume of A intersected with (A+x). Recently it has been proved that the covariogram determines any planar convex body, in the class of all convex bodies. We extend the class of sets in which a planar convex body is determined by its covariogram. Moreover, we prove that there is no pair of non-congruent planar polyominoes consisting of less than 9 points that have equal discrete covariogram., Comment: 15 pages, 7 figures, accepted for publication on Mathematika

Published
2010
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5. Aree e volumi: si può sempre misurare?

Author

Benassi, Carlo, Eleuteri, Michela, and Lussardi, Luca

Subjects
*INTEGRAL calculus, *MEASURE theory, *TEACHERS
Abstract

In this article, we intend to offer a starting point for thought regarding the concept of area, mainly addressing teachers: starting from simple considerations on equidecomposability of plane figures, we arrive to the notion of measure, a key tool for a correct foundation of the integral calculus. Moreover, we remark that the generality of the measure theory permits the existence of non-measurable figures, namely there are either figures with no area and with no volume. [ABSTRACT FROM AUTHOR]

Published
2023

12. Contributors

Author

Accardo, Agostino P., primary, Aiple, Franz, additional, Anderson, Tim, additional, Antonini, Riccardo, additional, Barnes, Graham R., additional, Beltrami, Giorgio, additional, Benassi, Carlo, additional, Bengelsdorf, Herbert, additional, Bergamaschi, Roberto, additional, Berthoz, Alain, additional, Paolo Biral, Gian, additional, Bonaventure, Nicole, additional, Bour, Lo J., additional, Braun, Doris, additional, Bruni, Rosa, additional, Callieco, Roberto, additional, Capocchi, Giuseppe, additional, Carmody, Dennis P., additional, Chekaluk, Eugene, additional, Cheron, Guy, additional, Citterio, Antonietta, additional, Tinsley Coble, E., additional, Corazza, Ruggero, additional, Cosi, Vittorio, additional, Crawford, Trevor J., additional, Da Pozzo, Stefano, additional, Dassonville, Paul, additional, De Angelis, Claudio, additional, dell'Aquila, Teresa, additional, Della Torre, Giovannella, additional, Draicchio, Francesco, additional, Duysens, Jacques, additional, d'Ydewalle, Géry, additional, Eadie, Andrew S., additional, Erkelens, Casper J., additional, Errico, Pierangelo, additional, Farrace, Stefano, additional, Ferraresi, Aldo, additional, Fetter, Michael, additional, Findlay, John M., additional, Fischer, Burkhart, additional, Flach, Frederich, additional, Fuchs, Albert F., additional, Galiana, Henrietta L., additional, Godaux, Emile, additional, Grassi, Silvarosa, additional, Grealy, Madeleine A., additional, Guitton, Daniel, additional, Harding, Anita E., additional, Heron, Gordon, additional, Hohnsbein, Joachim, additional, Horii, Ken, additional, Inchingolo, Paolo, additional, Israël, Isabelle, additional, Jagla, Fedor, additional, Jardon, Blandine, additional, Jüttner, Martin, additional, Kaplan, Melvin, additional, Kennard, Christopher, additional, Kim, Myoung-Soon, additional, Koenig, Eberhard, additional, Koken, Phil W., additional, Lefèvre, Philippe, additional, Ling, Leo, additional, Llewellyn, Keith R., additional, Lueck, Christian J., additional, Lui, Fausta, additional, Mateeff, Stefan, additional, Mergner, Thomas, additional, Mettens, Philippe, additional, Mossman, Stuart S., additional, de Visser, Bram W. Ongerboer, additional, Orlowski, Barbara, additional, Paré, Martin, additional, Pensiero, Stefano, additional, Perissutti, Paolo, additional, Pettorossi, Vito Enrico, additional, Phillips, James O., additional, Porcù, Silvio, additional, Pugh, John R., additional, Romani, Alfredo, additional, Roucoux, André, additional, Santarelli, Rosamaria, additional, Schlag, John, additional, Schlag-Rey, Madeleine, additional, Schweigart, Georg, additional, Spagno, Cinzia, additional, Speelman, Hans D., additional, Takeda, Mariko, additional, Tegetmeyer, Helmut, additional, Tweed, Douglas, additional, Uomori, Kenya, additional, Urbani, Luca, additional, van Gisbergen, Jan A.M., additional, Van Rensbergen, Johan, additional, van ′t Ent, Dennis, additional, Versino, Maurizio, additional, Waterston, John A., additional, Weber, Heike, additional, Wolf, Werner, additional, Wolzak, Adrie, additional, Worfolk†, Ralph, additional, Yakimoff, Naum, additional, Yamada, Mitsuho, additional, Yücel, Hasan Y., additional, Zambarbieri, Daniela, additional, Zampolini, Mauro, additional, and Zikmund, Vladislav, additional

Published
1994
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15. An Algorithm for Reconstructing a Convex Polygon from its Covariogram

Author

Benassi, Carlo 6/8/1962 and D'Ercole, Giuliana

Subjects
Convex polygon, Covariogram, Reconstructive procedure, Reconstructive Procedure, 52A10, Convex Polygon
Abstract

The covariogram of a compact convex set $K \subset \mathbb R^n$ is the function that at each point $x \in \mathbb R^n$ associates the volume of $K \cap (K + x)$. The covariogram determines, among all convex bodies, any planar convex polygon. In this paper we present an algorithm for reconstructing an arbitrary convex polygon from its covariogram.

Published
2007

23. STUDIES ON TRYPSIN INHIBITORS

Author

Tomatis, Roberto, primary, Guggi, Augusto, additional, Benassi, Carlo A., additional, Salvadori, Severo, additional, and Rocchi, Raniero, additional

Published
2009
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41. Sulfenyl Halides as Modifying Reagents for Polypeptides and Proteins.

Author

Boccú, Enrico, Veronese, Francesco M., Fontana, Angelo, and Benassi, Carlo A.

Subjects
HALIDES, SULFUR compounds, PEPTIDES, PROTEINS, TRYPTOPHAN, ACETIC acid
Abstract

The determination of tryptophan and cysteine content in proteins by means of the selective reaction of sulfenyl halides with these amino acids has been carefully investigated. By reaction with 2- or 4-nitrophenylsulfenyl chloride in aqueous acetic or formic acid, the nitrophenyl chromophore is covalently bound to the tryptophan and the cysteine residues of the protein, giving a thioether and a mixed disulfide respectively. The cysteine content has been determined spectrophotometrically at 450 nm from the 4-nitrothiophenol released from the mixed disulfides of the cysteine residues after exposure of the 4-nitrophenylsulfenyl chloride-labelled protein in 0.1 N NaOH (at this wavelength the corresponding chromophore covalently bound to tryptophan does not absorb). Tryptophan has been estimated in the sulfenylated proteins by spectrophotometric determinations at 365 or 328 nm of the 2- and 4-nitrophenylsulfenyl chromophores (εM 4000 and 11700 respectively), following removal of the yellow label from the cysteine residues, by dissolving the modified protein in 0.1 N NaOH. The procedure has been shown to be accurate for both amino acids with a wide variety of proteins. [ABSTRACT FROM AUTHOR]

Published
1970
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