| Dorin BUCUR
Professeur, membre de l'Institut Universitaire de France
Laboratoire de Mathématiques CNRS UMR 5127
ANR 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
Mathematical Theory in Fluid Mechanics
Kácov (Prague) May 22 - 29, 2015 (Pictures)
Calculus of Variations and PDEs
Le Bourget du Lac, September 24-25, 2015
| Isaac Newton Institute for Mathematical Sciences, Cambridge
Free Boundary Problems and Related Topics
6 January - 4 July 2014
Talk on isoperimetric inequalities and free discontinuity problems (video)
|List of publications (on MathSciNet)||Preprints|
Multiphase Free Discontinuity Problems: Monotonicity Formula and Regularity Results (with I. Fragalà and A. Giacomini), Preprint CVGMT 2018.
Local minimality results for the Mumford-Shah functional via monotonicity (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), Preprint CVGMT 2018.
Sign changing solutions of Poisson's equation (with M. Van den Berg), Preprint Arxiv 2018.
Optimal partitions for Robin Laplacian eigenvalues (with I. Fragalà and A. Giacomini), Preprint Arxiv 2018.
Maximization of the second non-trivial Neumann eigenvalue (with A. Henrot), Preprint CVGMT 2018.
Proof of the honeycomb asymptotics for optimal Cheeger clusters (with I. Fragalà), Preprint CVGMT 2017.
Best constant in Poincaré inequalities with traces: a free discontinuity approach (with A. Giacomini and P. Trebeschi), Preprint CVGMT 2017.
Phase field approach to optimal packing problems and related Cheeger clusters (with B. Bogosel and I. Fragalà), Applied Mathematics and Optimization (to appear), Preprint version on CVGMT 2017.
On the honeycomb conjecture for Robin Laplacian eigenvalues (with I. Fragalà), Communications in Contemporary Mathematics (to appear) 2018, 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. (to appear) Preprint version 2017.
Minimization of the k-th eigenvalue of the Robin Laplacian (with A. Giacomini), Preprint CVGMT 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.
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, (to appear) 2014.
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).