11 citations · 19 across the 16 of their papers we have counts for
16 papers
Heteroclinic connections for fractional Allen-Cahn equations with degenerate potentials
Francesco De Pas, Serena Dipierro, Mirco Piccinini +1
We investigate existence, uniqueness and asymptotic behavior of minimizers of a family of non-local energy functionals of the type $$ \frac{1}{4}\iint_{\mathbb{R}^{2n}\setminus (\m…
Bounded minimizers of double phase problems at nearly linear growth
Cristiana De Filippis, Filomena De Filippis, Mirco Piccinini
Bounded minimizers of double phase problems at nearly linear growth have locally Hölder continuous gradient within the sharp maximal nonuniformity range .
Regularity for multi-phase problems at nearly linear growth
Filomena De Filippis, Mirco Piccinini
Minima of the log-multiphase variational integral have locally Hölder continuous gradi…
De Giorgi-Nash-Moser theory for kinetic equations with nonlocal diffusions
Francesca Anceschi, Giampiero Palatucci, Mirco Piccinini
We extend the De Giorgi--Nash--Moser theory to nonlocal hypoelliptic equations arising in kinetic theory as linearized models for the non-cutoff Boltzmann equation. Assuming that t…
A limiting case in partial regularity for quasiconvex functionals
Mirco Piccinini
Local minimizers of nonhomogeneous quasiconvex variational integrals with standard -growth of the type feature almost everywhe…
Struwe's Global Compactness and energy approximation of the critical Sobolev embedding in the Heisenberg group
Giampiero Palatucci, Mirco Piccinini, Letizia Temperini
We investigate some of the effects of the lack of compactness in the critical Folland-Stein-Sobolev embedding in very general (possible non-smooth) domains, by proving via De Giorg…
Global Compactness, subcritical approximation of the Sobolev quotient, and a related concentration result in the Heisenberg group
Giampiero Palatucci, Mirco Piccinini, Letizia Temperini
We investigate some effects of the lack of compactness in the critical Sobolev embedding in the Heisenberg group.
Nonlinear fractional equations in the Heisenberg group
Giampiero Palatucci, Mirco Piccinini
We deal with a wide class of nonlinear nonlocal equations led by integro-differential operators of order , with summability exponent and differentiability…
Asymptotic approach to singular solutions for the CR Yamabe equation
Giampiero Palatucci, Mirco Piccinini
We study the loss of compactness for optimal functions of a subcritical approximations of the sharp Folland-Stein-Sobolev embedding in the Heisenberg group. When blow-up is prevent…
New perspectives on recent trends for Kolmogorov operators
Francesca Anceschi, Mirco Piccinini, Annalaura Rebucci
After carrying out an overview on the non Euclidean geometrical setting suitable for the study of Kolmogorov operators with rough coefficients, we list some properties of the funct…
Boundedness estimates for nonlinear nonlocal kinetic Kolmogorov-Fokker-Planck equations
Francesca Anceschi, Mirco Piccinini
We investigate local regularity properties of weak solutions to a broad class of nonlinear nonlocal kinetic Kolmogorov-Fokker-Planck equations. In particular, we focus on proving a…
Nonlocal Harnack inequalities in the Heisenberg group
Giampiero Palatucci, Mirco Piccinini
We deal with a wide class of nonlinear integro-differential problems in the Heisenberg-Weyl group , whose prototype is the Dirichlet problem for the -fractional su…
The obstacle problem and the Perron Method for nonlinear fractional equations in the Heisenberg group
Mirco Piccinini
We study the obstacle problem related to a wide class of nonlinear integro-differential operators, whose model is the fractional subLaplacian in the Heisenberg group. We prove both…
Hölder continuity and boundedness estimates for nonlinear fractional equations in the Heisenberg group
Maria Manfredini, Giampiero Palatucci, Mirco Piccinini +1
We extend the celebrate De Giorgi-Nash-Moser theory to a wide class of nonlinear equations driven by nonlocal, possibly degenerate, integro-differential operators, whose model is t…
Borderline global regularity for nonuniformly elliptic systems
Cristiana De Filippis, Mirco Piccinini
We establish sharp global regularity results for solutions to nonhomogeneous, nonunifomrly elliptic systems with zero boundary conditions. In particular, we obtain everywhere Lipsc…
The Dirichlet problem for a family of totally degenerate differential operators
Maria Manfredini, Mirco Piccinini, Sergio Polidoro
In the framework of Potential Theory we prove existence or the Perron-Weiner-Brelot-Bauer solution to the Dirichlet problem related to a family of totally degenerate, in the sense…