Page Web de Dorin Bucur



Professeur, membre senior honoraire de l'Institut Universitaire de France

Laboratoire de Mathématiques CNRS UMR 5127
Université de Savoie
Campus Scientifique
73 376 Le-Bourget-Du-Lac, France

 Tél:       +33 (0)4 79 75 86 29
 Fax:      +33 (0)4 79 75 81 42

 (replace _at_ by @)

Enseignement   Master de mathématiques Chambéry: Modélisation mathématique et analyse appliquée

Invited lecture at 9th European Congress of Mathematics, Seville July 15-19, 2024.

Symmetry-breaking of optimal shapes, American Institute of Mathematics, Passadena, June 17-21, 2024.

Shape Optimization and Isoperimetric and Functional Inequalities, Levico, September 18-22, 2023. (Link to the 2019 metting)

Research School on Shape Optimization, Spectral Geometry and Calculus of Variations, Luminy, March 23-April 2, 2021.

Isaac Newton Institute Cambridge
Geometric Spectral Theory and Applications

MSRI Berkeley
Free Boundary Problems, Theory and Applications
January 10, 2011 to May 20, 2011

Shape Optimization and Isoperimetric and Functional Inequalities, CIRM, November 21 - 25, 2016

Calculus of Variations and PDEs
Le Bourget du Lac, September 24-25, 2015

ANR GAOS research project, "Geometric analysis of optimal shapes"
Isaac Newton Institut Cambridge
Free Boundary Problems and Related Topics
6 January - 4 July 2014

Talk (video)

Mathematical Theory in Fluid Mechanics
Kácov (Prague) May 22-29, 2015

List of publications (on MathSciNet)
Preprints Arxiv 

Curriculum Vitae
Preprints CVGMT

Recent papers:

Sharp inequalities for Neumann eigenvalues on the sphere (with E. Martinet and M. Nahon), Journal of Differential Geometry (to appear), 2024 Preprint version on Arxiv.

The geometric size of the fundamental gap (with V. Amato and I. Fragalà), Preprint on CVGMT, 2024.

On the torsion function for simply connected, open sets in $\R^2$ (with M. Van den Berg), Preprint version on Arxiv, 2024.

Sharp Quantitative Stability of the Dirichlet spectrum near the ball (with J. Lamboley, M. Nahon and R. Prunier), Preprint on Arxiv, 2023.

On the Polygonal Faber-Krahn Inequality (with B. Bogosel), Journal de l'École Polytechnique — Mathématiques (to appear), 2023. Preprint on Arxiv.

The nonlocal isoperimetric problem for polygons: Hardy-Littlewood and Riesz inequalities (with B. Bogosel and I. Fragalà), Mathematische Annalen (to appear) Preprint on Arxiv, 2023.

Mean-to-max ratio of the torsion function and honeycomb structures (with L. Briani), Calc. Var. Partial Differential Equations 62 (2023), no. 7, Paper No. 198, 29 pp. Preprint version on Arxiv.

A free discontinuity approach to optimal profiles in Stokes flows (with A. Chambolle, A. Giacomini and M. Nahon), Annales de l’Institut Henri Poincaré, Analyse Non Linéaire (accepted) Preprint on Arxiv, 2023.

Boundary behavior of Robin problems in non-smooth domains (with A. Giacomini and M. Nahon), Preprint on Arxiv, 2022.

Maximization of Neumann Eigenvalues (with E. Martinet and E. Oudet), Arch. Ration. Mech. Anal. 247 (2023), no. 2, 19 Preprint on Arxiv, 2022.

On localisation of eigenfunctions of the Laplace operator (with M. Van den Berg), Preprint version on Arxiv.

Alexandrov theorem for general nonlocal curvatures: the geometric impact of the kernel (with I. Fragalà), Journal de Mathématiques Pures et Appliquées, Volume 169, January 2023, Pages 82-108. Preprint on Arxiv.
This is a companion paper to Rigidity for measurable sets.

Rigidity for measurable sets (with I. Fragalà), Advances in Mathematics Volume 414, 1 February 2023, 108862, Preprint on Arxiv.

Shape optimization of a thermal insulation problem (with M. Nahon, C. Nitsch and C. Trombetti), Calc. Var. Partial Differential Equations, 61 (2022), no. 5, Paper No. 186, Preprint on Arxiv.

Stability results for the Robin Laplacian on nonsmooth domains (with A. Giacomini and P. Trebeschi), SIAM Journal on Mathematical Analysis, 54 (2022), no. 4, 4591–4624, Preprint on CVGMT.

Degenerate free discontinuity problems and spectral inequalities in quantitative form (with A. Giacomini and M. Nahon), Arch. Ration. Mech. Anal., 242 (2021), no. 1, 453–483, Preprint on Arxiv.

Symmetry results for variational energies on convex polygons (with I. Fragalà), ESAIM: Control, Optimisation and Calculus of Variations, 27 (2021), No. 3, 16 pp, Preprint version on CVGMT.

Stability and instability issues of the Weinstock inequality (with M. Nahon), Transactions of the American Math. Soc.Volume 374, Number 3, March 2021, Pages 2201-2223, Preprint version on Arxiv.

Asymptotic behaviour of the Steklov problem on dumbbell domains (with A. Henrot and M. Michetti), Communications in PDE 46 (2021), no. 2, 362-393, Preprint version on Arxiv.

Weinstock inequality in higher dimensions (with V. Ferone, C. Nitsch and C. Trombetti), Journal of Differential Geometry 118 (2021), 1-21, Preprint version.

On efficiency and localisation for the torsion function (with M. Van den Berg and T. Kappeler), Potential Analysis Potential Analysis volume 57, pages 571–600 (2022), Preprint version on Arxiv.

L-infinity bounds of Steklov eigenfunctions and spectrum stability under domain variation (with A. Giacomini and P. Trebeschi), Journal of Differential Equations 269 (2020), no. 12, 11461–11491, Preprint version on CVGMT.

Sign changing solutions of Poisson's equation (with M. Van den Berg), Proc. London Math. Soc. (3) 121 (2020), no. 3, 513-536, Preprint version on Arxiv.

Maximization of the second non-trivial Neumann eigenvalue (with A. Henrot), Acta Math. 222 (2019), no. 2, 337–361.   Preprint version.

Proof of the honeycomb asymptotics for optimal Cheeger clusters (with  I. Fragalà), Advances in Mathematics 350 (2019), 97–129, Preprint version.

Local minimality results for the Mumford-Shah functional via monotonicity (with I. Fragalà and A. Giacomini), Analysis & PDE 13 (2020), no. 3, 865-899, Preprint version.

Minimization of the k-th eigenvalue of the Robin Laplacian (with A. Giacomini), Journal of Functional Analysis 277 (2019), no. 3, 643–687, Preprint version.

The multiphase Mumford-Shah problem (with I. Fragalà and A. Giacomini), SIAM Journal on Imaging Sciences 12 (2019), no. 3, 1561-1583, Preprint version.

A sharp estimate for the first Robin-Laplacian eigenvalue with negative boundary parameter  (with V. Ferone, C. Nitsch and C. Trombetti),  Rendiconti Lincei Matematica e Applicazioni 30 (2019), no. 4, 665-676, Preprint Arxiv.

Multiphase Free Discontinuity Problems: Monotonicity Formula and Regularity Results (with I. Fragalà and A. Giacomini), Annales I. H. Poincaré, Analyse non linéaire, (2020) online first Preprint CVGMT.

Geometric control of the Robin Laplacian eigenvalues: the case of negative boundary parameter  (with S. Cito), J. of Geometric Analysis 30 (2020), no. 4, 4356-4385, Preprint CVGMT.

Optimal partitions for Robin Laplacian eigenvalues (with I. Fragalà and A. Giacomini), Calculus of Variations and PDEs  57 (2018), no. 5, Art. 122, Preprint version.

Best constant in Poincaré inequalities with traces: a free discontinuity approach (with A. Giacomini and P. Trebeschi), Annales I. H. Poincaré 36 (2019), no. 7, 1959-1986 Preprint CVGMT.

Phase field approach to optimal packing problems and related Cheeger clusters (with B. Bogosel and  I. Fragalà), Applied Mathematics and Optimization (2018) [link to the journal], Preprint  version on CVGMT 2017.

On the honeycomb conjecture for Robin Laplacian eigenvalues (with  I. Fragalà), Communications in Contemporary Mathematics 21 (2019), no. 2, 1850007, 29 pp., Preprint version.

Two optimization problems in thermal insulation (with G. Buttazzo and C. Nitsch),  Notices Amer. Math. Soc. 64 (2017), no. 8, 830–835.

Optimal shapes maximizing the Steklov eigenvalues (with B. Bogosel and A. Giacomini), SIAM J. Math. Analysis  49 (2017), no. 2, 1645-1680.  Preprint version.

On the honeycomb conjecture for a class of minimal convex partitions (with  I. Fragalà, B. Velichkov and G. Verzini), Transactions of the A.M.S. 370 (2018), no. 10, 7149–7179 Preprint  version.

The quantitative Faber-Krahn inequality for the  Robin Laplacian (with V. Ferone, C. Nitsch and C. Trombetti), Journal of Differential Equations 264 (2018), no. 7, 4488–4503, (, Preprint version.

Reverse Faber-Krahn and Mahler inequalities for the Cheeger constant (with I. Fragalà) Proceedings A of The Royal Society of Edinburgh  (2018), no. 5, 913–937, Preprint version.

A new isoperimetric inequality for the elasticae (with A. Henrot), J. Eur. Math. Soc. 19, 3355–3376, 2017, Preprint version on Arxiv.

Existence results, (book chapter, open access) Shape optimization and spectral theory, 13–28, De Gruyter Open, Warsaw, 2017.

The Robin problem (with P. Freitas and J. Kennedy) (book chapter, open access) Shape optimization and spectral theory, 78–119, De Gruyter Open, Warsaw, 2017.

The Robin Laplacian problem on varying domains (with A. Giacomini and P. Trebeschi), Calculus of Variations and PDEs  55 (2016), no. 6, 55:133, Preprint version on CVGMT.

Symmetry breaking for a problem in optimal insulation (with G. Buttazzo and C. Nitsch), Journal de Mathématiques Pures et Appliquées (9) 107 (2017), no. 4, 451–463, Preprint version on Arxiv.

Maximizing Neumann Eigenvalues on Rectangles (with M. Van den Berg and K. Gittins) Bulletin of the London Mathematical Society  48 (2016), no. 5, 877–894, Preprint Arxiv 2015.

A free boundary approach to the Faber-Krahn inequality (with P. Freitas) (book chapter) Geometric and Computational Spectral Theory, 73–86, Contemp. Math., 700, Amer. Math. Soc., Providence, RI, 2017. Preprint version.

Blaschke-Santalo and Mahler inequalities for the first eigenvalue of the Dirichlet Laplacian (with I. Fragalà), Proceedings of the London Mathematical Society (3) 113 (2016), no. 3, 387-417, Preprint version.

The Saint-Venant inequality for the Laplace operator with Robin boundary conditions (with A. Giacomini),  Milan J. Math. 83 (2015), no. 2, 327–343, Preprint version.

Shape optimization problems with Robin conditions on the free boundary (with A. Giacomini), Annales I. H. Poincaré 2016,  no. 6, 1539-1568, Preprint version on CVGMT.

A surgery result for the spectrum of the Dirichlet Laplacian (with D. Mazzoleni),  SIAM J. Math. Anal. 47 (2015), no. 6, 4451-4466, Preprint version on CVGMT.

Faber-Krahn inequalities for the Robin-Laplacian: a free discontinuity approach (with. A. Giacomini),  Arch. Ration. Mech. Anal. 218 (2015), no. 2, 757–824, Preprint version on CVGMT.

A Faber-Krahn inequality for the Cheeger constant of N-gons (with. I. Fragalà),  J. Geom. Anal. 26 (2016), no. 1, 88–117, Preprint version on CVGMT.

Lipschitz regularity of the eigenfunctions on optimal domains (with. D. Mazzoleni, A. Pratelli and B. Velichkov), Arch. Ration. Mech. Anal., 2014 (DOI) 10.1007/s00205-014-0801-6, Preprint version on CVGMT.

Spectral optimization problems for potentials and measures (with. G. Buttazzo and B. Velichkov), SIAM Journal of Mathematical Analysis, 46 (2014), no. 4, 2956–2986, Preprint version on CVGMT.

Hand written notes of the course "Shape optimization and isoperimetric inequalities, Napoli, September 9-13, 2013.

Monotonicity formula and  regularity for general free discontinuity problems (with S. Luckhaus), Arch. Ration. Mech. Anal.  211 (2014) 489–511,  Preprint version opn CVGMT.

Multiphase shape optimization problems (with. B. Velichkov), SIAM Journal on Control and Optimization, 52 (2014), no. 6, 3556–3591.

On the torsion function with Robin or Dirichlet boundary conditions (with M. Van den Berg), Journal of Functional Analysis (2013),, Preprint version.

Asymptotic behaviour of optimal spectral planar domains with fixed perimeter (with P. Freitas),  J. Math. Phys. 54, 053504 (2013), Preprint version.

Minimization of eigenvalues by free boundary - free discontinuity methods, Oberwolfach workshop "Geometric Aspects of Spectral Theory", July 2012, Oberwolfach Reports 2012.

Hand written notes of the course on "Existence of optimal shapes", Scuola Normale Superiore Pisa, June 3-8 2012

Minimization of the k-th eigenvalue of the Dirichlet Laplacian, Arch. Ration. Mech. Anal. 206 (2012) 1073-1083, 2012, Preprint version on CVGMT.

Lower bounds for the Prékopa-Leindler deficit by some distances modulo translations (with I. Fragala),  Journal of Convex Analysis, Vol. 21 (2014), Preprint version.

Shape optimization problems with internal constraint (with G. Buttazzo and B. Velichkov), Ann. I. H. Poincaré – AN 30 (2013) 477--495, Preprint version on CVGMT.

Shape flows for spectral optimization problems   (with G. Buttazzo and U. Stefanelli),  Interfaces Free Bound. 14 (2012), no. 4, 521--544, Preprint version on CVGMT.

Optimal convex shapes for concave functionals (with I. Fragala and J. Lamboley),  ESAIM Control Optim. Calc. Var. 18 (2012), no. 3, 693--711, Preprint version on CVGMT.

The first biharmonic Steklov eigenvalue: the positivity preserving and shape optimization (with Filippo Gazzola)  Milan Journal of Mathematics, Volume 79,  1 (2011),  247--258. Preprint version.

Micro shape control, riblets and drag  minimization (with M. Bonnivard), SIAM J. Appl. Math. 73-2 (2013), pp. 723--740,  Preprint version on Hal.

A variational approach to the isoperimetric inequality for the Robin eigenvalue problem (with A. Giacomini), Arch. Ration. Mech. Anal. Volume 198, Number 3, 927--961, 2010, Preprint version on CVGMT.

The uniform rugosity effect (with M. Bonnivard), to appear in J. Math. Fluid Mech., 14 (2012), no. 2, 201–215, Preprint version on Hal.

On the characterization of the compact embedding of Sobolev spaces  (with G. Buttazzo), Calculus of Variations and PDEs 44 (2012), no. 3-4, 455-475, Preprint version on CVGMT.

Boundary behavior of viscous fluids: Influence of wall roughness and friction-driven boundary conditions (with E. Feireisl, S. Necasova) Arch. Ration. Mech. Anal. 197 (2010), 117--138, Preprint version.

Optimal partitions for eigenvalues (with B. Bourdin, E. Oudet) SIAM J. of Scientific Computing 31  (2009/10),  no. 6, 4100--4114 Preprint version.

How to Choose Interpolation Data in Images (with Z. Belhachmi, B. Burgeth, J. Weickert), SIAM J. of Appl. Maths.  70  (2009),  no. 1, 333--352.,  Preprint version.

An alternative approach to the Faber-Krahn inequality for Robin problems (with D. Daners)Calculus of Variations and PDEs  37  (2010),  no. 1-2, 75--86, Preprint version.

Minimization of $\lambda_2 (\Omega)$ with a perimeter constraint (with G. Buttazzo and  A. Henrot) Indiana University Mathematics Journal Vol. 58, (6) 2009, 2709--2728. Preprint version.

The rugosity effect, Jindrich Necas Center for Mathematical Modeling Lecture Notes Volume 5 "Qualitative properties of solutions to partial differential equations", E. Feireisl, P. Kaplicky and J. Malek Editors, 1--24,  2009 (survey of the talks given at the Necas Center for Mathematical Modeling, Prague).

On the first eigenvalue of a fourth order Steklov problem (with A. Ferrero and F. Gazzola),  Calculus of Variations and PDEs 35 (2009), 103--131. Preprint version.

On the asymptotic limit of the Navier-Stokes system with rough boundaries (with E. Feireisl, S. Necasova and J. Wolf), Journal of Differential Equations,  244  (2008),  no. 11, 2890--2908Preprint version.

Quasistatic Evolution in Debonding Problems via Capacitary Methods (with G. Buttazzo and A. Lux)Arch. Ration. Mech. Anal. 190  (2008),  no. 2, 281--306. Preprint version.

On the asymptotic limit of flows past a ribbed boundary (with E. Feireisl and S. Necasova), J. Math. Fluid Mech.  10  (2008),  no. 4, 554--568. Preprint version.

Influence of wall roughness on the slip behavior of viscous fluids (with E. Feireisl and S. Necasova), Proc. Royal Soc. Edinburgh Sec. A. 138  (2008),  no. 5, 957--973..  Preprint version.

Whitney property in two dimensional Sobolev spaces  (with A. Giacomini and P. Trebeschi), Proc. Amer. Math. Soc.  136 (2008), 2535--2545. Preprint version.

Do optimal shapes exist? (survey of the talk given at Seminario Matematico Fisico di Milano, November 2006, Milan Journal of Mathematics, 75 (2007), 379--398.) Preprint version.

Irreversible quasistatic evolutions by minimizing movements  (with G. Buttazzo), Journal of Convex Analysis (link to the Journal), 15 (3), July 2008. Preprint version.

The incompressible limit of the full Navier-Stokes-Fourier system on domains with rough boundaries (with E. Feireisl), Nonlinear Analysis: Real World Applications, 10 (2009), 3203--3229 (link to the journal). Preprint version.

The eigenvalue problem with conductivity boundary conditions (with I. Durus and E. Oudet)  Control and Cybernetics  37  (2008),  no. 4, 811--829.  Preprint version.

Stability and uniqueness for the crack identification problem  (with Z. Belhachmi) (SIAM J. Control and Optimization 46  (2007),  no. 1, 253--273. ) Preprint version.

Characterization of the shape stability for nonlinear elliptic problems (Journal of Differential Equations, 226 (2006), no. 1, 99--117). Preprint version.

Weak semi-continuity of the duality product in Sobolev spaces ( J. Funct. Anal. 236 (2006), no. 2, 712--725). Preprint version.

Shape optimization problems for eigenvalues of elliptic operators (Zeitschrift für Angewandte Mathematik und Mechanik, 86 (2006), no. 3, 171--184) (joint paper with Z. Belhachmi,  G. Buttazzo and J.-M. Sac-Epée). Please send an e-mail for a reprint.

Asymptotic analysis and scaling of friction parameters (with Ioan R. Ionescu) (Zeitschrift für Angewandte Mathematik und Physik, 2005). Please send an e-mail for a reprint.

How to prove existence in shape optimization (Control and Cybernetics 34 (2005), no. 1, 103--116). Preprint version.

Finite element approximation of the Neumann eigenvalue problem in domains with multiple cracks  (with Z. Belhachmi and J.-M. Sac-Epée) ( IMA J. of Numerical Analysis,  26  (2006),  no. 4, 790--810).

Book: Variational Methods in Shape Optimization Problems
(with G. Buttazzo) 
Series: Progress in Nonlinear Differential Equations and Their Applications, Vol. 65 , Birkhäuser 2005

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