Page Web de Dorin Bucur




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

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ANR research project
"Geometric analysis of optimal shapes"

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

Geometric Functional Inequalities and Shape Optimization

Naples, September 9th-13th, 2013

Isaac Newton Institute for Mathematical Sciences, Cambridge
Free Boundary Problems and Related Topics
6 January - 4 July 2014

List of publications (on MathSciNet)

Curriculum Vitae

Recent papers:

Faber-Krahn inequalities for the Robin-Laplacian: a free discontinuity approach (with. A. Giacomini), Preprint CVGMT, January 2014.

A Faber-Krahn inequality for the Cheeger constant of N-gons (with. I. Fragala), Preprint CVGMT, January 2014.

Lipschitz regularity of the eigenfunctions on optimal domains (with. D. Mazzoleni, A. Pratelli and B. Velichkov), Preprint CVGMT, December 2013.

Spectral optimization problems for potentials and measures (with. G. Buttazzo and B. Velichkov), Preprint CVGMT October 2013.

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.

Multiphase shape optimization problems (with. B. Velichkov), April 2013.

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

A new proof of the Faber-Krahn inequality and the symmetry of optimal domains for higher eigenvalues (with P. Freitas), September 2012.

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), to appear in  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--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).,,5-10044-22-36290509-0,00.html

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

Table of contents



Groupe de travail

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