Homepage of Bozhidar Velichkov

Maître de conférences, Université Grenoble Alpes

I am working in the fields of Calculus of Variations and Partial Differental Equations. My recent research is concentrated mainly in the areas of:
Free Boundary Problems
Multiphase and Optimal Partition Problems
Spectral Optimization Problems

I am currently part of the team Calculus of Variations, Geometry and Images (CVGI) at Laboratoire Jean Kuntzmann (LJK).

Below you can find information on my
CV, List of Pubblications , Research topics, Research projects, Teaching,
as well as information on the CVGI seminar and some useful Links.


• Since September 2014, Maître de conférences at Université Grenoble Alpes.

• In 2014 I was a post-doc at the Universtity of Pisa.

• From 2010 to 2013 I was a Ph.D. student at Scuola Normale Superiore and since 2012 also at Université de Savoie . My thesis was prepared under the direction of Giuseppe Buttazzo and Dorin Bucur.

• From 2005 to 2010 I was a student at SNS.


Free Boundary Problems

Regularity of minimizers of shape optimization problems involving perimeter

(with Guido De Philippis, Jimmy Lamboley and Michel Pierre, JMPA 2017)

A free boundary problem arising in PDE optimization

(with Giuseppe Buttazzo and Edouard Oudet, Calc.Var.PDE 2016)

Lipschitz Regularity of the Eigenfunctions on Optimal Domains

(with Dorin Bucur, Dario Mazzoleni and Aldo Pratelli, Arch. Rat. Mech. Anal. 2015)

A Note on the Monotonicity Formula of Caffarelli-Jerison-Kenig

(Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat.Appl. 2014)

Multiphase and Optimal Partition Problems

On the honeycomb conjecture for a class of minimal convex partitions (with Dorin Bucur, Ilaria Fragalà and Gianmaria Verzini, 2017)

Spectral and Shape Optimization Problems

Worst-case shape optimization for the Dirichlet energy

(with J. C. Bellido and Giuseppe Buttazzo, Nonlinear Analysis 2016)

Spectral Optimization Problems for Potentials and Measures

(with Dorin Bucur and Giuseppe Buttazzo, SIAM J. Math. Anal. 2014)

Optimal Potentials for Schrodinger Operators (with Giuseppe Buttazzo, Augusto Gerolin and Berardo Ruffini, Journal de l'École polytechnique — Mathématiques 2014)

Shape Optimization Problems for Metric Graphs

(with Giuseppe Buttazzo and Berardo Ruffini, ESAIM: COCV 2014)

Spectral Optimization Problems with Internal Constraint

(with Dorin Bucur and Giuseppe Buttazzo, Ann.Inst.H.P. 2013)

Further topics in Calculus of Variations and PDE

Numerical Calibration of Steiner trees

(with Annalisa Massaccesi and Edouard Oudet, Appl. Math. Optim. 2017)

BV estimates in optimal transportation and applications

(with Guido De Philippis, Alpar Meszaros and Filippo Santambrogio, ARMA 2015)

Faber-Krahn inequalities in sharp quantitative form

(with Lorenzo Brasco and Guido De Philippis, Duke Math. J. 2015)

Review articles, proceedings and book chapters

Spectral optimization problems for Schrödinger operators (with Giuseppe Buttazzo, Chapter 9 from the book Shape Optimization and Spectral Theory, De Gruyter 2017)

The spectral drop problem
(with Giuseppe Buttazzo, Contemporary mathematics 666, 2016)

A free boundary approach to shape optimization problems

(with Dorin Bucur, Philosophical Transactions of the Royal Society of London A 2015)

Optimization problems involving the first Dirichlet eigenvalue and the torsional rigidity (with Giuseppe Buttazzo and Michiel van den Berg, Chapter from the book New Trends in Shape Optimization 2015)

Some New Problems in Spectral Optimization

(with Giuseppe Buttazzo, Banach Center Publications 2014)




PI of the project VARIFORM - Méthodes variationnelles en optimisation de formes (JUNE 2015 - DEC 2016) dedicated to several existence and regularity issues arising in shape optimization with respect to the spectrum of the Laplacian with Dirichlet and Neumann boundary conditions. The project was financed by Université Grenoble Alpes as part of the support program AGIR-POLE-MSTIC.


19 june 2017, Grenoble
Worshop GeoSpec


Under construction

CVGI seminar

The seminar Calculus of Variations, Geometry and Image takes place on Thursdays at 11h00 at LJK and is jointly organized with Charles Dapogny.


CVGMT - Calculus of Variations and Geometric Measure Theory

Analysis of PDEs