| Dorin BUCUR
Professeur, membre senior honoraire de l'Institut Universitaire de France
Laboratoire de Mathématiques CNRS UMR 5127
|Research School on Shape Optimization, Spectral Geometry and Calculus of Variations, Luminy, March 23-April 2, 2021 (local webpage)|
Shape Optimization and Isoperimetric and Functional Inequalities, Levico, September 23-27, 2019
ANR GAOS research project, "Geometric analysis of optimal shapes"
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
| Isaac Newton Institut Cambridge
Free Boundary Problems and Related Topics
6 January - 4 July 2014
Mathematical Theory in Fluid Mechanics
Kácov (Prague) May 22 - 29, 2015 (Pictures)
|List of publications (on MathSciNet)||Preprints|
Rigidity for measurable sets (with I. Fragalà), Preprint on Arxiv, 2021.
Degenerate free discontinuity problems and spectral inequalities in quantitative form (with A. Giacomini and M. Nahon), Preprint on Arxiv, 2020.
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.
On efficiency and localisation for the torsion function (with M. Van den Berg and T. Kappeler), Potential Analysis, (2021) accepted, 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 Arxiv.
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.
Weinstock inequality in higher dimensions (with V. Ferone, C. Nitsch and C. Trombetti), Journal of Differential Geometry (to appear), 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 https://doi.org/10.1016/j.anihpc.2020.12.003 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, (https://doi.org/10.1016/j.jde.2017.12.014), Preprint version.
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.
Symmetry breaking for a problem in optimal design (with G. Buttazzo and C. Nitsch), Journal de Mathématiques Pures et Appliquées (9) 107 (2017), no. 4, 451–463, Preprint version.
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.
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.
Monotonicity formula and regularity for general free discontinuity problems (with S. Luckhaus), Arch. Ration. Mech. Anal. 211 (2014) 489–511, Preprint version.
Multiphase shape optimization problems (with. B. Velichkov), SIAM Journal on Control and Optimization, 52 (2014), no. 6, 3556–3591.
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.
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.
Shape flows for spectral optimization problems (with G. Buttazzo and U. Stefanelli), Interfaces Free Bound. 14 (2012), no. 4, 521--544, Preprint version.
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.
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.
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.The uniform rugosity effect (with M. Bonnivard), to appear in J. Math. Fluid Mech., 14 (2012), no. 2, 201–215, Preprint version.
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.
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--2908. Preprint 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.
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
e-mail for a
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).