[velichkov]

Full Professor, Università di Pisa

**Email:** *bozhidar.velichkov AT unipi.it*

**Home-page:** http://www.velichkov.it/

**arxiv id:** velichkov_b_1

- M. Colombo - L. Spolaor - B. Velichkov (Accepted Paper:
*Interfaces and Free Boundaries*)

Almost everywhere uniqueness of blow-up limits for the lower dimensional obstacle problem (2021) - G. Buttazzo - F. P. Maiale - B. Velichkov (Submitted Paper)

Shape optimization problems in control form (2021) - F. Générau - E. Oudet - B. Velichkov (Preprint)

Cut locus on compact manifolds and uniform semiconcavity estimates for a variational inequality (2020) - F. Générau - E. Oudet - B. Velichkov (Preprint)

Numerical computation of the cut locus via a variational approximation of the distance function (2020) - S. Guarino Lo Bianco - D. A. La Manna - B. Velichkov (Accepted Paper:
*Journal de l'École polytechnique - Mathématiques*)

A two-phase problem with Robin conditions on the free boundary (2020) - D. Mazzoleni - B. Trey - B. Velichkov (Preprint)

Regularity of the optimal sets for the second Dirichlet eigenvalue (2020) - G. De Philippis - L. Spolaor - B. Velichkov (Preprint)

Regularity of the free boundary for the two-phase Bernoulli problem (2019) - B. Velichkov (Lecture Notes)

Regularity of the one-phase free boundaries (2019) - E. Russ - B. Trey - B. Velichkov (Accepted Paper:
*Calc. Var. PDE*)

Existence and regularity of optimal shapes for elliptic operators with drift (2019) - M. Engelstein - L. Spolaor - B. Velichkov (Accepted Paper:
*Geom. Topol.*)

(Log-)epiperimetric inequality and regularity over smooth cones for almost Area-Minimizing currents (2018) - L. Spolaor - B. Trey - B. Velichkov (Accepted Paper:
*Communications in Partial Differential Equations*)

Free boundary regularity for a multiphase shape optimization problem (2018) - M. Colombo - L. Spolaor - B. Velichkov (Accepted Paper:
*J. Reine Agnew. Math.*)

On the asymptotic behavior of the solutions to parabolic variational inequalities (2018) - M. Engelstein - L. Spolaor - B. Velichkov (Accepted Paper:
*Duke Math. J.*)

Uniqueness of the blow-up at isolated singularities for the Alt-Caffarelli functional (2018) - D. Mazzoleni - S. Terracini - B. Velichkov (Accepted Paper:
*Analysis & PDE*)

Regularity of the free boundary for the vectorial Bernoulli problem (2018) - L. Spolaor - B. Velichkov (Accepted Paper:
*Comm. Pure Appl. Math.*)

An epiperimetric inequality for the regularity of some free boundary problems: the $2$-dimensional case (2017) - M. Colombo - L. Spolaor - B. Velichkov (Accepted Paper:
*Geom. Funct. Anal.*)

A logarithmic epiperimetric inequality for the obstacle problem (2017) - D. Mazzoleni - S. Terracini - B. Velichkov (
*Geom. Funct. Anal.*)

Regularity of the optimal sets for some spectral functionals (2017) - D. Bucur - I. Fragalà - G. Verzini - B. Velichkov (Accepted Paper:
*Trans. Amer. Math. Soc.*)

On the honeycomb conjecture for a class of minimal convex partitions (2017) - G. Buttazzo - B. Velichkov (Accepted Paper:
*SIAM J. Math. Anal.*)

A shape optimal control problem and its probabilistic counterpart (2017) - G. Buttazzo - B. Velichkov (Book Chapter)

Spectral optimization problems for Schrödinger operators (2017) - M. Colombo - L. Spolaor - B. Velichkov (Accepted Paper:
*Comm. Pure Appl. Math.*)

Direct epiperimetric inequalities for the thin obstacle problem and applications (2017) - G. Buttazzo - F. Maestre - B. Velichkov (
*Journal of Optimization Theory and Applications*)

Optimal potentials for problems with changing sign data (2017) - J. C. Bellido - G. Buttazzo - B. Velichkov (
*Nonlinear Analysis*)

Worst-case shape optimization for the Dirichlet energy (2016) - A. Massaccesi - E. Oudet - B. Velichkov (
*Appl. Math. Optim.*)

Numerical Calibration of Steiner trees (2016) - G. De Philippis - J. Lamboley - M. Pierre - B. Velichkov (
*J. Math. Pures Appl.*)

Regularity of Minimizers of Shape Optimization Problems involving Perimeter (2016) - L. Brasco - G. De Philippis - B. Velichkov (
*Duke Math. J.*)

Faber-Krahn inequalities in sharp quantitative form (2015) - G. De Philippis - A. R. Mészáros - F. Santambrogio - B. Velichkov (Accepted Paper:
*Arch. Ration. Mech. An.*)

BV Estimates in Optimal Transportation and Applications (2015) - G. Buttazzo - E. Oudet - B. Velichkov (
*Calc. Var. PDE*)

A free boundary problem arising in PDE optimization (2015) - D. Bucur - D. Mazzoleni - A. Pratelli - B. Velichkov (
*Arch. Rat. Mech. Anal.*)

Lipschitz regularity of the eigenfunctions on optimal domains (2015) - G. Buttazzo - M. van den Berg - B. Velichkov (Preprint)

Optimization problems involving the first Dirichlet eigenvalue and the torsional rigidity (2014) - B. Velichkov (
*Rend. Lincei Mat. Appl.*)

A note on the monotonicity formula of Caffarelli-Jerison-Kenig (2014) - G. Buttazzo - B. Velichkov (Preprint)

The spectral drop problem (2014) - G. Buttazzo - B. Ruffini - B. Velichkov (
*ESAIM Control Optim. Calc. Var.*)

Shape Optimization Problems for Metric Graphs (2014) - D. Bucur - G. Buttazzo - B. Velichkov (
*SIAM J. Math. Anal.*)

Spectral optimization problems for potentials and measures (2014) - G. De Philippis - B. Velichkov (
*Appl. Math. Optim.*)

Existence and regularity of minimizers for some spectral functionals with perimeter constraint (2014) - D. Bucur - B. Velichkov (
*SIAM J. Control Optim.*)

Multiphase shape optimization problems (2014) - B. Velichkov (Phd Thesis)

Existence and regularity results for some shape optimization problems (2013) - D. Bucur - G. Buttazzo - B. Velichkov (
*Ann. I. H. Poincare' Anal. Non Lineaire*)

Shape Optimization Problems with Internal Constraint (2013) - G. Buttazzo - A. Gerolin - B. Ruffini - B. Velichkov (
*J. Éc. polytech. Math.*)

Optimal Potentials for Schrödinger Operators (2013) - G. Buttazzo - B. Velichkov (
*J. Funct. Anal.*)

Shape optimization problems on metric measure spaces (2013) - B. Bogosel - B. Velichkov (
*SIAM Numer. Anal.*)

A multiphase shape optimization problem for eigenvalues: qualitative study and numerical results (2013) - G. Buttazzo - B. Velichkov (Preprint)

Some New Problems in Spectral Optimization (2012)

*4 mar 2021:*Vectorial free boundary problems*6 nov 2019:*Regularity of the two-phase free boundaries.*7 feb 2018:*Un approccio variazionale alla regolarità delle frontiere libere singolari*25 may 2011:*Concentration-compactness principle and shape optimization problems

*16 jan 2020 - 17 jan 2020:*Geometric Measure Theory in Padova*31 may 2019 - 31 may 2019:*Brescia - Trento Nonlinear Day - Ed. III*27 may 2019 - 30 may 2019:*Analytic and Geometric Aspects of PDEs*24 apr 2017 - 26 apr 2017:*Transport problems in Zurich*25 oct 2016 - 28 oct 2016:*Workshop in Geometric Measure Theory, Shape Optimisation and Free Boundaries