Research interests
Research topics: Boundary Value Problems in irregular domains
(fractals, (epsilon,delta), d-sets).
a)
Linear and quasilinear Venttsel’ problems on pre-fractal and fractal
domains:
1.
Existence, uniqueness and regularity of the weak solutions;
2.
Asymptotic behavior of the solutions;
3.
Numerical approximation of Venttsel’ problems in pre-fractal domains.
b)
Robin-Venttsel’ problems for (nonlinear) fractional operators on
pre-fractal and fractal domains:
1.
Existence, uniqueness and regularity of the weak solutions;
2.
Asymptotic behavior of the solutions.
c)
Problems of mathematical physics on pre-fractal and fractal domains:
1.
Magnetostatic problems;
2.
Stokes problems;
3.
Compactness properties of magnetic operators (Friedrichs and Gaffney
inequalities).
Papers and other products:
[15] S. Creo, M. R. Lancia, Dynamical boundary
conditions for time-dependent fractional operators on extension domains, under
review. Available on arXiv: https://arxiv.org/abs/2205.06656
[14] S. Creo, M. R. Lancia, The p-curl system in extension domains, under review.
[13] S. Creo, M. R. Lancia, P.
Vernole, Transmission problems for the fractional
p-Laplacian across fractal interfaces, Discrete Cont. Dyn. Syst. Series S, 15 (12), (2022), 3621-3644.
[12] S. Creo, Singular
p-homogenization for highly conductive fractal layers, Z. Anal. Anwendungen, 40
(4), (2021), 401-424.
[11] S. Creo, M. R. Lancia, Fractional
(s,p)-Robin-Venttsel’ problems on extension domains, NoDEA Nonlinear
Differential Equations Appl., 28 (3), (2021), paper no. 31, 33 pp.
[10] M. Cefalo, S. Creo, M.
Gallo, M. R. Lancia, P. Vernole, Approximation of 3D Stokes flows in fractal domains, in:
Fractals in Engineering: Theoretical Aspects and Numerical Approximation, SEMA
SIMAI Springer Series vol. 8, Spinger-Cham, (2021), 27-53.
[9] S. Creo, M. R. Lancia, P.
Vernole, M-Convergence
of p-fractional energies in irregular domains, J. Convex Analysis, 28
(2), (2021), 509-534.
[8] S. Creo, M. R. Lancia, A.
I. Nazarov, Regularity
results for nonlocal evolution Venttsel’ problems, Fract. Calc. Appl.
Anal., 23 (5), (2020), 1416-1430.
[7] S. Creo, M. Hinz, M. R.
Lancia, A. Teplyaev, P. Vernole, Magnetostatic problems in
fractal domains, in: Fractals and Dynamics
for Mathematics, Science and the Arts, Volume 5: Analysis, Probability and
Mathematical Physics on Fractals, World Scientific, (2020), 477-502.
[6] S. Creo, M. R. Lancia, Friedrichs inequality in irregular
domains, J. Math. Anal. Appl., 484 (1), (2020), 123665.
[5] S. Creo, M. R. Lancia, P.
Vernole, Convergence of fractional diffusion processes
in extension domains, J. Evol. Equ., 20 (1), (2020), 109-139.
[4] M. Cefalo, S. Creo, M. R.
Lancia, P. Vernole, Nonlocal Venttsel’ diffusion in fractal-type
domains: regularity results and numerical approximation, Math. Methods
Appl. Sci., 42 (14), (2019), 4712-4733.
[3] S. Creo, V. Regis Durante,
Convergence
and density results for parabolic quasi-linear Venttsel’ problems in fractal
domains, Discrete Cont. Dyn. Syst. Series S, 12 (1), (2019), 65-90.
[2] S. Creo, M. R. Lancia, A.
Nazarov, P. Vernole, On two-dimensional nonlocal Venttsel’
problems in piecewise smooth domains, Discrete Cont. Dyn. Syst. Series
S, 12 (1), (2019), 57-64.
[1] S. Creo, M. R. Lancia, A.
Vélez-Santiago, P. Vernole, Approximation of
a nonlinear fractal energy functional on varying Hilbert spaces, Commun. Pure Appl. Anal., 17 (2),
(2018), 647–669.
[*] S. Creo, Local
and nonlocal Venttsel’ problems in fractal domains, PhD Thesis. Supervisor:
Maria Rosaria Lancia.