Draft:Filippo Chiarenza

• Comment: Only cites primary sources. Devonian Wombat (talk) 14:29, 20 August 2025 (UTC)

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Filippo Chiarenza

Filippo Chiarenza (Catania, July 3, 1951 – Catania, July 11, 1996) was an Italian mathematician known for his contributions in the field of partial differential equations, particularly for the results obtained with Michele Frasca and Placido Longo on the regularity of solutions in spaces with vanishing mean oscillation (VMO) coefficients.

Biography

He graduated with honors in Mathematics in 1973 from the University of Catania, with a thesis titled “Maximum principle for weak subsolutions of second-order elliptic equations”, under the supervision of Francesco Guglielmino.

After graduation, he held positions as a research fellow, grant holder, and eventually as an ordinary assistant in Advanced Analysis at the Faculty of Mathematical, Physical and Natural Sciences of the University of Catania. After passing the national qualification exam required by Article 37 of Presidential Decree No. 382/1980, he was appointed Associate Professor of Mathematics for Biological Sciences in 1985.

In 1987 he became Associate Professor of Mathematical Analysis at the University of Messina, where he worked for two years. He returned to the University of Catania in November 1989, joining the Faculty of Engineering, and was appointed Full Professor of Mathematical Analysis on May 18, 1990.

He passed away on July 11, 1996, at the age of 45, due to pleural mesothelioma.

Scientific activity

Introduced to research by his thesis advisor Francesco Guglielmino, he also collaborated with Eugene Fabes during a research stay at the Institute for Mathematics and its Applications at the University of Minnesota. He also served as a visiting professor at Princeton and Chicago.

His research focused mainly on elliptic and parabolic partial differential equations, as well as real analysis.

In collaboration with Michele Frasca and Placido Longo, he gave an optimal solution to a longstanding problem posed by Carlo Miranda in 1963 in the journal Annali di Matematica Pura e Applicata (63 (1963), pp. 353–386), regarding the regularity of solutions to the Dirichlet problem for second-order linear nonvariational elliptic equations. The main results were published in the following works:

• F. Chiarenza, M. Frasca, P. Longo, $W^{2,p}$ estimates for non divergence elliptic equations with discontinuous coefficients, Ricerche di Matematica, 40 (1991), pp. 149–168.
• F. Chiarenza, M. Frasca, P. Longo, $W^{2,p}$-solvability of the Dirichlet problem for nondivergence elliptic equations with VMO coefficients, Trans. Amer. Math. Soc., 336 (1993), pp. 841–853.

These results, obtained by considering coefficients in the function space VMO (Vanishing Mean Oscillation)—a more refined setting than that originally proposed by Miranda—have had a significant impact in the mathematical literature.

The presence of some of his former students, now tenured professors at the University of Catania, highlights the formative legacy left by Filippo Chiarenza, despite the brevity of his career.

Honors

Room 22 of the Department of Mathematics and Computer Science at the University of Catania, where Filippo Chiarenza taught his final class during the academic year 1995–1996, is now dedicated to his memory.

Legacy and Recognition

The scientific contributions of Filippo Chiarenza have been recognized internationally.

His life and work were commemorated in several tributes, including obituaries in the Notiziario dell’Unione Matematica Italiana, the Bollettino Mathesis – Sezione di Catania, as well as a trigesimo notice published in the newspaper La Sicilia.

Several conferences have been organized in his memory, including:

• International Conference on Boundary Value Problems for Elliptic and Parabolic Operators, in memory of Filippo Chiarenza, November 12–14, 1998, Department of Mathematics, University of Catania.

Speakers included G. Alessandrini, A. Alvino, O. Arena, L. Boccardo, B. Franchi, N. Garofalo, M. Krbec, E. Lanconelli, S. Salsa, C. Sbordone, R. Serapioni, C.G. Simader, G. Talenti, G. Trombetti, and R. Wheeden.

• International Conference, Fabes–Chiarenza Lectures 2002, December 2–4, 2002, Siracusa, Italy.

Speakers included H. Beresticky, B. Franchi, N. Garofalo, M. Giaquinta, C. Gutierrez, C. Kenig, M. Mitrea, J. Pipher, A. Ruiz, and C. Sbordone.

• International Conference in Memory of Filippo Chiarenza – A Day on PDEs, June 14, 2016, Department of Mathematics and Computer Science, University of Catania.

Speakers included B. Franchi, C. Gutierrez, E. Lanconelli, S. Salsa, R. Serapioni, and V. Vespri.

• International Conference on Degenerate Elliptic Operators and Applications, in memory of Filippo Chiarenza, November 12, 2021, Department of Mathematics and Computer Science, University of Catania.

Speakers included B. Franchi, N. Garofalo, and R. Serapioni.