Full Professor, Università di Pisa

Email: bozhidar.velichkov AT unipi.it

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

arxiv id: velichkov_b_1

Available papers (60):

[plain text]

• L. Ferreri - L. Spolaor - B. Velichkov (preprint)
  On the fine structure of the solutions to nonlinear thin two-membrane problems in 2D (2024)
• L. Ferreri - L. Spolaor - B. Velichkov (preprint)
  On the boundary branching set of the one-phase problem (2024)
• L. Ferreri - L. Spolaor - B. Velichkov (preprint)
  Unique continuation for nonlinear variational problems (2024)
• R. Ognibene - B. Velichkov (preprint)
  Boundary regularity of the free interface in spectral optimal partition problems (2024)
• G. Bevilacqua - S. Stuvard - B. Velichkov (preprint)
  Classical solutions to the soap film capillarity problem for plane boundaries (2024)
• B. Velichkov (Lecture Notes: Lecture Notes of the Unione Matematica Italiana, Springer)
  Regularity of the one-phase free boundaries (2023)
• N. Edelen - L. Spolaor - B. Velichkov (Preprint)
  The symmetric (log-)epiperimetric inequality and a decay-growth estimate (2023)
• L. Ferreri - B. Velichkov (preprint)
  A one-sided two phase Bernoulli free boundary problem (2023)
• L. Ferreri - B. Velichkov (preprint)
  Regularity for one-phase Bernoulli problems with discontinuous weights and applications (2023)
• L. Ferreri - G. Tortone - B. Velichkov (preprint)
  A capillarity one-phase Bernoulli free boundary problem (2023)
• D. Mazzoleni - G. Tortone - B. Velichkov (J. Convex Analysis)
  On the dimension of the singular set in optimization problems with measure constraint (2023)
• S. Guarino Lo Bianco - D. A. La Manna - B. Velichkov (Submitted Paper)
  Free boundary cluster with Robin condition on the transmission interface (2022)
• N. Edelen - L. Spolaor - B. Velichkov (Accepted Paper: Indiana Math. J.)
  A strong maximum principle for minimizers of the one-phase Bernoulli problem (2022)
• F. Générau - E. Oudet - B. Velichkov (Accepted Paper: Arch. Rat. Mech. Anal.)
  Cut locus on compact manifolds and uniform semiconcavity estimates for a variational inequality (2022)
• D. Mazzoleni - B. Trey - B. Velichkov (Ann. Inst. H. Poincaré Anal. Non Linéaire)
  Regularity of the optimal sets for the second Dirichlet eigenvalue (2022)
• G. Buttazzo - F. P. Maiale - D. Mazzoleni - G. Tortone - B. Velichkov (Arch. Rat. Mech. Anal.)
  Regularity of the optimal sets for a class of integral shape functionals (2022)
• 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)
• G. De Philippis - M. Engelstein - L. Spolaor - B. Velichkov (Preprint)
  Rectifiability and almost everywhere uniqueness of the blow-up for the vectorial Bernoulli free boundaries (2021)
• F. P. Maiale - G. Tortone - B. Velichkov (Accepted Paper: Revista Matemática Iberoamericana)
  Epsilon-regularity for the solutions of a free boundary system (2021)
• F. P. Maiale - G. Tortone - B. Velichkov (Accepted Paper: Annali della Scuola Normale Superiore di Pisa, Classe di Scienze)
  The boundary Harnack principle on optimal domains (2021)
• G. De Philippis - L. Spolaor - B. Velichkov (Inventiones mathematicae)
  Regularity of the free boundary for the two-phase Bernoulli problem (2021)
• L. Spolaor - B. Velichkov (Mathematics in Engineering)
  On the logarithmic epiperimetric inequality for the obstacle problem (2021)
• G. De Philippis - L. Spolaor - B. Velichkov (Accepted Paper: J. Eur. Math. Soc.)
  (Quasi-)conformal methods in two-dimensional free boundary problems (2021)
• 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 (Journal de l'École polytechnique - Mathématiques)
  A two-phase problem with Robin conditions on the free boundary (2020)
• E. Russ - B. Trey - B. Velichkov (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)

Seminars:

• 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

Speaker:

• 16 sep 2024 - 20 sep 2024: Workshop "Calculus of Variations: a New Generation"
• 17 jun 2024 - 21 jun 2024: Geometric Measure Theory and applications 2024
• 20 may 2024 - 22 may 2024: 50 Anni di Calcolo delle Variazioni
• 22 jan 2024 - 26 jan 2024: New Trends in Nonlinear PDE's, Physics and Geometry
• 29 may 2023 - 2 jun 2023: Geometric Measure Theory, Bressanone 2023
• 20 feb 2023 - 22 feb 2023: New Trends in Geometric & Variational PDEs
• 8 jun 2022 - 10 jun 2022: Geometric Analysis and PDE on Garda Lake
• 30 aug 2021 - 3 sep 2021: Geometric Measure Theory and applications
• 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

Organizer:

• 20 may 2024 - 22 may 2024: 50 Anni di Calcolo delle Variazioni
• 11 apr 2024 - 12 apr 2024: Calculus of Variations and Free Boundary Problems VIII
• 5 mar 2024 - 5 mar 2024: Calculus of Variations and Free Boundary Problems VII
• 31 jan 2024 - 2 feb 2024: Workshop "Regularity and geometric aspects of nonlinear PDEs"
• 5 oct 2023 - 5 oct 2023: Calculus of Variations and Free Boundary Problems VI
• 28 mar 2023 - 28 mar 2023: Calculus of Variations and Free Boundary Problems V
• 8 nov 2022 - 8 nov 2022: Calculus of Variations and Free Boundary Problems IV
• 13 jun 2022 - 17 jun 2022: Shape Optimization, related topics and applications