LAMBERTI PIER DOMENICO

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Scientific sector MAT/05 - MATHEMATICAL ANALYSIS
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Notice and additional information
First prize by the Department of Industrial Engineering of the University of Padova for the best student evaluation for the lecture course Calculus 2 for the Degree Course in Chemical and Material Engineering, Academic Year 2017-2018.

Office hours
Su appuntamento
(updated on 04/07/2013 23:00)

Proposals for thesis
1) Michele Zaccaron, Phd in Mathematics, under supervision.

2) Francesco Ferraresso, Phd in Mathematics, 2018. Title: “On the spectral stability of polyharmonic operators on singularly perturbed domains”.

3) Luigi Provenzano, Phd in Mathematics, 2016. Title: “On mass distribution and concentration phenomena for linear elliptic partial differential operators”.

4) Davide Buoso, Phd in Mathematics, 2015. Title: “Shape sensitivity analysis of the eigenvalues of polyharmonic operators and elliptic systems”.

5) Ivan Yuri Violo (A.Y. 2016-2017), Master Thesis. Title: “Extension operators on
Sobolev-Morrey spaces”. 110/110 cum Laude.

6) Francesco Ferraresso (A.Y. 2013-2014), Master Thesis (co-supervision with Prof. Jari Taskinen, University of Helsinki, Erasmus Program). Title: “Singular perturbation problems for a class of partial differential equations in a double-periodic perforated plane”. 110/110 cum Laude.

7) Francesco Ferraresso (A.Y. 2011-2012), Bachelor dissertation. Title: “L'equazione del p-laplaciano”. 110/110 cum Laude.

8) Luigi Provenzano (A.Y. 2010-2011), Master Thesis. Title: “Eigenvalues of harmonic and poly-harmonic operators subject to mass density perturbations”. 110/110 cum Laude.

9) Gianluigi Potente (A.Y. 2010-2011), Master Thesis (co-supervision with Prof. Marco Marletta della Cardiff University, UK, Erasmus Program). Title: “On spectrum of a dissipatively perturbed Schrödinger operator on the real semi-axis”. 110/110 cum Laude.

10) Davide Buoso (A.Y. 2010-2011), Master Thesis. Title: “On the spectral stability of poly-harmonic operators on variable domains”. 110/110 cum Laude.

11) Matteo Basei (A.Y. 2009-2010), Bachelor Dissertation. Title: “Su alcune stime di stabilita' spettrale per operatori differenziali alle derivate parziali di tipo ellittico”. 110/110 cum Laude.

12) Luigi Provenzano (A.Y. 2008-2009), Bachelor Dissertation. Title: “Sulla dipendenza dello spettro di una membrana vibrante dalla densita' di massa”. 106/110.

13) Giacomo Drago (A.Y. 2008-2009), Bachelor Dissertation. Title: “Funzioni e funzioni strane: alcuni aspetti storici e didattici”. 110/110 cum Laude.

14) Marco Perin (A.Y. 2008-2009), Bachelor Dissertation. Title: “Sulla ottimalita' di alcune stime di stabilita' spettrale per operatori differenziali ellittici del secondo ordine”. 110/110.

15) Giovanni Franzina (A.Y. 2008-2009), Master Thesis. Title: “On a class of nonlinear eigenvalue problems. Existence, Uniqueness and stability results”. 110/110 e Lode. Posizione attuale: assegnista di ricerca, Istituto Nazionale di Alta Matematica “F. Severi”, Unità di ricerca di Firenze.

16) Mandorino Vito Nicola (A.Y. 2006-2007), Bachelor Disseration (co-supervisin with Prof. Victor Burenkov). Title: “On a General Spectral Stability Theorem and some applications to the Laplace Operator”. 110/110 cum Laude.

Curriculum Vitae
Professional Experience

10 May 2019: National Scientific Habilitation to Full Professor in Mathematical Analysis
1 September 2015 - present: Associate Professor in Mathematical Analysis at the University of Padova
1 March 2006 - 30 August 2015: Researcher in Mathematical Analysis at the University of Padova
1 October 2010 - 30 September 2017: Tutor in Mathematical Analysis at the school of excellence of the University of Padova - Scuola Galileiana di Studi Superiori.

Education

Phd in Mathematics University of Padova, 2003
Laurea in Mathematics University of Padova, 1998, Summa cum Laude

Research visits

Long term visits: University of Cardiff, University of Athens, Complutense University of Madrid
Short term visits: People's Friendship University of Russia (Moscow), Technion Israel Institute of Tecnology (Haifa, Isreael), EPFL École polytechnique fédérale de Lausanne, University of Paris 7, BCAM in Bilbao, Luleå University of Technology (Sweden), Eurasian National University (Astana, Kazakhstan), University of Crete, University of Ioannina, University of Catania, University of Aveiro.

Invited talks

About fifty invited talks and seminars at international meetings and research institutes in Italy, Russia, US, Japan, Switzerland, UK, France, Germany, Spain, Portugal, Greece, Czech Republic, Poland, Bulgaria, Israel, Turkey, Kazakhstan.


Research areas
Research field

Mathematical Analysis

Areas of interest

Partial Differential Equation, Spectral theory, Theory of functions spaces, Functional Analysis, Calculus of variations, Homogenization theory.

Research topics

Perturbation problems for elliptic partial differential operators of second and higher order
Shape sensitivity analysis, spectral stability estimates and optimization
Boundary homogenization for polyharmonic operators
Mass concentration phenomena and Steklov-type problems
Eigenvalue problems for quasilinear equations
Spectral theory for time-harmonic Maxwell's equations
Hardy inequalities
Extension theorems for Sobolev-Morrey spaces on Lipschitz domains
Pathological functions and pathological function spaces

Publications
Recent Publications

Ferrero, Alberto; Lamberti, Pier Domenico; Spectral stability for a class of fourth order Steklov problems under domain perturbations, Calculus of Variations and Partial Differential Equations Vol. 58 (2019), 33, 1-57.

Lamberti, Pier Domenico; Violo, Ivan Yuri; On Stein's extension operator preserving Sobolev-Morrey spaces. To appear in Math. Nachr.

Lamberti, Pier Domenico; Pinchover, Yehuda; Lp Hardy inequality on C1,γ domains. To appear in Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) Vol. XIX, no. 3, 2019.

Arrieta, José M.; Ferraresso, Francesco; Lamberti, Pier Domenico; Boundary homogenization for a triharmonic intermediate problem, Math. Methods Appl. Sci. 41 (2018), no. 3, 979–985.

Arrieta, José M.; Ferraresso, Francesco; Lamberti, Pier Domenico; Spectral analysis of the biharmonic operator subject to Neumann boundary conditions on dumbbell domains, Integral Equations and Operator Theory, 89 (2017), no. 3, 377–408.

Arrieta, José M.; Lamberti, Pier Domenico; Higher order elliptic operators on variable domains. Stability results and boundary oscillations for intermediate problems, J. Differential Equations 263 (2017), no. 7, 4222–4266.

Lamberti, Pier Domenico; Provenzano, Luigi; Neumann to Steklov eigenvalues: asymptotic and monotonicity results. Proc. Roy. Soc. Edinburgh Sect. A 147 (2017), no. 2, 429–447.

Fanciullo, Maria Stella; Lamberti, Pier Domenico On Burenkov's extension operator preserving Sobolev-Morrey spaces on Lipschitz domains. Math. Nachr. 290 (2017), no. 1, 37–49.

Lamberti, Pier Domenico; Stefani, Giorgio Sobolev subspaces of nowhere bounded functions. Real Anal. Exchange 41 (2016), no. 2, 367–375.

Barbatis, Gerassimos; Lamberti, Pier Domenico Monotonicity, continuity and differentiability results for the Lp Hardy constant. Israel J. Math. 215 (2016), no. 2, 1011–1024.

Buoso, Davide; Lamberti, Pier Domenico Shape sensitivity analysis of the eigenvalues of the Reissner-Mindlin system. SIAM J. Math. Anal. 47 (2015), no. 1, 407–426.

Barbatis, Gerassimos; Lamberti, Pier Domenico Shape sensitivity analysis of the Hardy constant. Nonlinear Anal. 103 (2014), 98–112.

Lamberti, Pier Domenico Steklov-type eigenvalues associated with best Sobolev trace constants: domain perturbation and overdetermined systems. Complex Var. Elliptic Equ. 59 (2014), no. 3, 309–323.

Buoso, Davide; Lamberti, Pier Domenico Shape deformation for vibrating hinged plates. Math. Methods Appl. Sci. 37 (2014), no. 2, 237–244.

Lamberti, P. D.; Provenzano, L. A maximum principle in spectral optimization problems for elliptic operators subject to mass density perturbations. Eurasian Math. J. 4 (2013), no. 3, 70–83.

Buoso, Davide; Lamberti, Pier Domenico Eigenvalues of polyharmonic operators on variable domains. ESAIM Control Optim. Calc. Var. 19 (2013), no. 4, 1225–1235.

Arrieta, José M.; Lamberti, Pier Domenico Spectral stability results for higher-order operators under perturbations of the domain. C. R. Math. Acad. Sci. Paris 351 (2013), no. 19-20, 725–730.

Barbatis, Gerassimos; Lamberti, Pier Domenico Spectral stability estimates for elliptic operators subject to domain transformations with non-uniformly bounded gradients. Mathematika 58 (2012), no. 2, 324–348.

Burenkov, Victor I.; Lamberti, Pier Domenico Sharp spectral stability estimates via the Lebesgue measure of domains for higher order elliptic operators. Rev. Mat. Complut. 25 (2012), no. 2, 435–457.

List of taught course units in A.Y. 2019/20
Degree course code (?) Degree course track Course unit code Course unit name Credits Year Period Lang. Teacher in charge
SC2094 COMMON SCP4063454 12 1st Year (2019/20) First
semester
ITA PAOLO MUSOLINO
SC2095 COMMON SCP4063454 12 1st Year (2019/20) First
semester
ITA PAOLO MUSOLINO
SC1159 COMMON SCP6076297 6 3rd Year (2019/20) Second
semester
ITA PIER DOMENICO LAMBERTI
SC1159 COMMON SCL1001040 14 2nd Year (2019/20) Annual ITA ROBERTO MONTI