Dorin BUCUR
Professeur, membre senior honoraire de l'Institut Universitaire de France Laboratoire de Mathématiques CNRS UMR 5127
email dorin.bucur_at_univsavoie.fr

List of publications (on MathSciNet)  Preprints  
Curriculum Vitae  Research 
Recent papers:
Degenerate free discontinuity problems and spectral inequalities in quantitative form (with A. Giacomini and M. Nahon), Preprint on Arxiv, 2020.
Stability and instability issues of the Weinstock inequality (with M. Nahon), Transactions of the American Math. Soc. (to appear) 2020, Preprint on Arxiv, 2020.
Asymptotic behaviour of the Steklov problem on dumbbell domains (with A. Henrot and M. Michetti), Communications in PDE (to appear) 2020, Preprint on Arxiv, 2020.
On efficiency and localisation for the torsion function (with M. Van den Berg and T. Kappeler), Preprint on Arxiv 2020.
Linfinity bounds of Steklov eigenfunctions and spectrum stability under domain variation (with A. Giacomini and P. Trebeschi), Journal of Differential Equations (to appear) 2020, Preprint version.
Sign changing solutions of Poisson's equation (with M. Van den Berg), Proc. London Math. Soc. (to appear) 2020, Preprint version on Arxiv.
Maximization of the second nontrivial 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 MumfordShah functional via monotonicity (with I. Fragalà and A. Giacomini), Analysis & PDE (to appear), Preprint version.
Minimization of the kth eigenvalue of the Robin Laplacian (with A. Giacomini), Journal of Functional Analysis 277 (2019), no. 3, 643–687, Preprint version.
The multiphase MumfordShah problem (with I. Fragalà and A. Giacomini), SIAM Journal on Imaging Sciences (to appear) 2019, Preprint version.
A sharp estimate for the first RobinLaplacian eigenvalue with negative boundary parameter (with V. Ferone, C. Nitsch and C. Trombetti), Rendiconti Lincei Matematica e Applicazioni (to appear), Preprint Arxiv 2018.
Multiphase Free Discontinuity Problems: Monotonicity Formula and Regularity Results (with I. Fragalà and A. Giacomini), Preprint CVGMT 2018.
Geometric control of the Robin Laplacian eigenvalues: the case of negative boundary parameter (with S. Cito), J. of Geometric Analysis (to appear) 2019, 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 (to appear) 2019 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, 16451680. 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 FaberKrahn 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 FaberKrahn inequality (with P. Freitas) (book chapter) Geometric and Computational Spectral Theory, 73–86, Contemp. Math., 700, Amer. Math. Soc., Providence, RI, 2017. Preprint version.
BlaschkeSantalo 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, 387417, Preprint version.A surgery result for the spectrum of the Dirichlet Laplacian (with D. Mazzoleni), SIAM J. Math. Anal. 47 (2015), no. 6, 44514466, 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 38 2012
Minimization of the kth eigenvalue of the Dirichlet Laplacian, Arch. Ration. Mech. Anal. 206 (2012) 10731083, 2012, Preprint version.
Lower bounds for the PrékopaLeindler 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) 477495, Preprint version.
Shape flows for spectral optimization problems (with G. Buttazzo and U. Stefanelli), Interfaces Free Bound. 14 (2012), no. 4, 521544, Preprint version.
Optimal convex shapes for concave functionals (with I. Fragala and J. Lamboley), ESAIM Control Optim. Calc. Var. 18 (2012), no. 3, 693711, Preprint version.
The first biharmonic Steklov eigenvalue: the positivity preserving and shape optimization (with Filippo Gazzola) Milan Journal of Mathematics, Volume 79, 1 (2011), 247258. Preprint version.
Micro shape control, riblets and drag minimization (with M. Bonnivard), SIAM J. Appl. Math. 732 (2013), pp. 723740, 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, 927961, 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. 34, 455475, Preprint version.
Boundary behavior of viscous fluids: Influence of wall roughness and frictiondriven boundary conditions (with E. Feireisl, S. Necasova) Arch. Ration. Mech. Anal. 197 (2010), 117138, Preprint version.
Optimal partitions for eigenvalues (with B. Bourdin, E. Oudet) SIAM J. of Scientific Computing 31 (2009/10), no. 6, 41004114 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, 333352., Preprint version.
An alternative approach to the FaberKrahn inequality for Robin problems (with D. Daners), Calculus of Variations and PDEs 37 (2010), no. 12, 7586, 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, 27092728. 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, 124, 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), 103131. Preprint version.
On the asymptotic limit of the NavierStokes system with rough boundaries (with E. Feireisl, S. Necasova and J. Wolf), Journal of Differential Equations, 244 (2008), no. 11, 28902908. Preprint version.
Quasistatic Evolution in Debonding Problems via Capacitary Methods (with G. Buttazzo and A. Lux), Arch. Ration. Mech. Anal. 190 (2008), no. 2, 281306. 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, 554568. 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, 957973.. Preprint version.Weak semicontinuity of the duality product
in Sobolev spaces ( J. Funct.
Anal. 236 (2006), no. 2, 712725). Preprint version.
Shape optimization problems
for eigenvalues of
elliptic operators (Zeitschrift
für Angewandte Mathematik und Mechanik, 86
(2006),
no. 3, 171184) (joint
paper with Z. Belhachmi, G.
Buttazzo and
J.M. SacEpée). Please send an email for a
reprint.
Asymptotic analysis and
scaling of friction
parameters (with Ioan R. Ionescu) (Zeitschrift für Angewandte
Mathematik und Physik, 2005). Please send
an
email for a
reprint.
How to prove existence in shape optimization (Control and Cybernetics, 34 (2005), no. 1, 103116). Preprint version.
Finite element approximation of the Neumann eigenvalue problem in domains with multiple cracks (with Z. Belhachmi and J.M. SacEpée) ( IMA J. of Numerical Analysis, 26 (2006), no. 4, 790810).
