6 papers · 1 filter
On the mean value property of fractional harmonic functions
Claudia Bucur, Serena Dipierro, Enrico Valdinoci
As well known, harmonic functions satisfy the mean value property, namely the average of the function over a ball is equal to its value at the center. This fact naturally raises th…
Minimisers of a fractional seminorm and nonlocal minimal surfaces
Claudia Bucur, Serena Dipierro, Luca Lombardini +1
The recent literature has intensively studied two classes of nonlocal variational problems, namely the ones related to the minimisation of energy functionals that act on functions…
The stickiness phenomena of nonlocal minimal surfaces: new results and a comparison with the classical case
Claudia Bucur
We discuss in this note the stickiness phenomena for nonlocal minimal surfaces. Classical minimal surfaces in convex domains do not stick to the boundary of the domain, hence examp…
Approximate convexity principles and applications to PDEs in convex domains
Claudia Bucur, Marco Squassina
We obtain approximate convexity principles for solutions to some classes of nonlinear elliptic partial differential equations in convex domains involving approximately concave nonl…
Asymptotic mean value properties for fractional anisotropic operators
Claudia Bucur, Marco Squassina
We obtain an asymptotic representation formula for harmonic functions with respect to a linear anisotropic nonlocal operator. Furthermore we get a Bourgain-Brezis-Mironescu type li…
Some nonlocal operators and effects due to nonlocality
Claudia Bucur
In this PhD thesis, we deal with problems related to nonlocal operators, in particular to the fractional Laplacian and to some other types of fractional derivatives (the Caputo and…