Research
Publications:
P.D. Lamberti, P. Luzzini, M. Zaccaron. Permittivity optimization for Maxwell's eigenvalues. Submitted.
M. Zaccaron. A remark on the Hadamard-Hirakawa formula for an electromagnetic cavity problem. Boll. Unione Mat. Ital. (2023).
C. Bernardini, V. Vespri, M. Zaccaron. A note on Campanato’s Lp-regularity of solutions of elliptic equations with continuous coefficients. Eurasian Math. J. 13 (2022), no. 4, 44–53.
P. Luzzini, M. Zaccaron . A few results on permittivity variations in electromagnetic cavities. Journal of Differential Equations 334 (2022), 342–367.
P.D. Lamberti, M. Zaccaron. Spectral stability of the curl curl operator via uniform Gaffney inequalities on perturbed electromagnetic cavities. Mathematics in Engineering (2023), Vol. 5 Issue 1, pp. 1-31.
P.D. Lamberti, M. Zaccaron. Shape sensitivity for electromagnetic cavities. Mathematical Methods in the Applied Sciences Volume 44 (2021), Issue 13, pp. 10477-10500.
R. Monti, M. Zaccaron, Height estimate and Lipschitz approximation for geodesics in Carnot groups. Matematiche 75, no. 1 (2020), pp. 91-103.
Talks:
“Electromagnetic frequencies in a bounded domain” - Young Researchers in Functional Analysis and Mathematical Physics’23, University of Évora (Portugal), July 17 2023.
“Permittivity perturbations for time-harmonic Maxwell’s equations” - Mini-courses in Mathematical Analysis 2023, Padova (Italy), June 19 2023.
“Shape sensitivity analysis of a Maxwell’s cavity problem” - MAFIA Student conference, Telč (Czech Republic), 18 May 2023.
“On a Maxwell cavity problem” - MAFIA seminar (Methods of Algebra and Functional Analysis In Applications), FNSPE building of the Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague (Czech Republic), 2 May 2023.
“Spectral sensitivity analysis for electromagnetic cavities” - Oberseminar Analysis, Fakultät Mathematik, Institut für Analysis, TU Dresden (Germany), 3 June 2022.
“Spectral sensitivity analysis for electromagnetic cavities” - 100 UMI 800 UNIPD - First UMI meeting of PhD students, session of "Equazioni a derivate parziali". Department of Mathematics, University of Padova (Italy), 26 May 2022.
“Sensitivity analysis of Maxwell's equations in a cavity” - 13th ISAAC congress, session of “Constructive Methods in the Theory of Composite and Porous Media". Ghent (Belgium), 5 August 5 2021.
“A differential eigenproblem of electromagnetics” - Seminario Dottorato, Department of Mathematics, University of Padova (Italy), 3 March 2021.
“Domain perturbation theory: results in spectral shape optimization via a functional analytic approach” - Young Researchers Colloquium, IMPAN, Warsaw (Poland), 4 December 2020.
“Spectral stability for the Maxwell equations in a cavity” - Shape Optimization and Isoperimetric and Functional Inequalities, Levico Terme (Italy), 24 September 2019.
“Spectral stability for the Maxwell equations in a cavity ” - 12th ISAAC congress, session of “Spectral Theory of Partial Differential Equations”. Aveiro (Portugal) 30 July 2019.
Research interests:
Functional analysis
Maxwell's equations
Spectral theory
Elliptic theory of PDEs
Homogenization theory and asymptotic analysis
Calculus of Variations
Geometric measure theory
Ongoing projects:
Spectral analysis in electromagnetic waveguides.
Bounds for the Maxwell eigenvalues in bounded domains.
Homogenization theory and asymptotic analysis for time-harmonic Maxwell's equations in a perfectly conducting cavity.
Optimization problems for the electric permittivity in electromagnetic cavities.