Page Web de Dorin Bucur
Enseignement
Recent papers:
Multiphase shape optimization problems (with. B. Velichkov), April 2013.
On the torsion function with Robin or Dirichlet boundary conditions (with M. Van den Berg), May 2013.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).
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
Monotonicity formula and regularity for general free discontinuity problems (with S. Luckhaus), Preprint CVGMT March 2012.
Minimization of the k-th eigenvalue of the Dirichlet Laplacian, Arch. Ration. Mech. Anal. 206 (2012) 1073-1083, 2012.
Lower bounds for the Prékopa-Leindler deficit by some distances modulo translations (with I. Fragala), Journal of Convex Analysis, Vol. 21 (2014).
Shape optimization problems with internal constraint (with G. Buttazzo and B. Velichkov), J. Math. Pures et Appl. 2012 (to appear).
Shape flows for spectral optimization problems (with G. Buttazzo and U. Stefanelli), Interfaces Free Bound. 14 (2012), no. 4, 521--544.
Optimal convex shapes for concave functionals (with I. Fragala and J. Lamboley), ESAIM Control Optim. Calc. Var. 18 (2012), no. 3, 693--711.
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.
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.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.
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.
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).
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