All my preprints and papers are available on ArXiv and CVGMT.


P R E P R I N T S 

[2025]  A priori Hölder estimates for equations degenerating on nodal sets
\w S. Terracini and S. Vita

[2025]  Smoothness and stability in the Alt-Phillips problem
\w M. Carducci

[2025]  Some remarks on singular capillary cones with free boundary
\w A. Pacati and B. Velichkov

[2024]  A priori regularity estimates for equations degenerating on nodal sets
\w S. Terracini and S. Vita

[2023]  A capillarity one-phase Bernoulli free boundary problem
\w L. Ferreri and B. Velichkov

  
P U B L I C A T I O N S 

[2024]  Regularity of the optimal sets for a class of integral shape functionals
\w G. Buttazzo, F.P. Maiale, D. Mazzoleni and B. Velichkov
Arch. Rat. Mech. Anal. 248 (44)

            Higher order boundary Harnack principle via degenerate equations
\w S. Terracini and S. Vita
Arch. Rat. Mech. Anal. 248 (29)

            Liouville theorems and optimal regularity in elliptic equations
G. Tortone
Proc. Lond. Math. Soc. 128 (3)

            On the nodal set of solutions to some sublinear equations without homogeneity
\w N. Soave
Arch. Rat. Mech. Anal. 248 (26)

[2023]  On the dimension of singular set in optimization problems with measure constraint
\w D. Mazzoleni and B. Velichkov
J. Convex. Anal. 31 (2)

            A vectorial problem with thin free boundary
\w D. De Silva
Calc. Var. Partial Differential Equations. 62 (221)

            Epsilon-regularity for the solutions of a free boundary system
\w F.P. Maiale and B. Velichkov
Rev. Mat. Iberoamericana. 39 (5)

[2022]  The boundary Harnack principle on optimal domains
\w F.P. Maiale and B. Velichkov
Ann. Sc. Norm. Super. Pisa Cl. Sci. 25 (1)

            The nodal set of solutions to some nonlocal sublinear problems
G. Tortone
Calc. Var. Partial Differential Equations. 61 (82)

[2021]  Regularity of shape optimizers for some spectral fractional problems
G. Tortone
J. Funct. Anal. 281 (12)

[2020]  On the nodal set of solutions to degenerate or singular elliptic equations with an application to s-harmonic functions
\w Y. Sire and S. Terracini
J. Math. Pures Appl. 143, 376 - 441

            Improvement of fatness for vector valued free boundary problems
\w D. De Silva
Math. Eng. 2 (4)

            Regularity results for segregated configurations involving fractional Laplacians
\w A. Zilio
Nonlinear Anal. 193

[2018]  On s-harmonic functions on cones
\w S. Terracini and S. Vita
Anal. PDE. 11 (7)

  
P R O C E E D I N G S  A N D  S U R V E Y S 

[2025]  Vectorial Bernoulli problems and free boundary systems
\w. B. Velichkov
In preparation

[2020]  The nodal set of solutions to anomalous equations
G. Tortone
Bruno Pini Math. Anal. Semin. 10 (1)