44 research outputs found
The Abresch-Gromoll inequality in a non-smooth setting
We prove that the Abresch-Gromoll inequality holds on infinitesimally
Hilbertian CD(K,N) spaces in the same form as the one available on smooth
Riemannian manifolds
A non-smooth Brezis-Oswald uniqueness result
We classify the non-negative critical points in of where is convex and positively
-homogeneous, while is non-increasing.
Since may not be differentiable and has a one-sided growth condition,
is only l.s.c. on . We employ a weak notion of critical
point for non-smooth functionals, derive sufficient regularity of the latter
without an Euler-Lagrange equation available and focus on the uniqueness part
of the results in \cite{BO}, through a non-smooth Picone inequality.Comment: 30 pages, comments welcome
Nonlocal problems at critical growth in contractible domains
We prove the existence of a positive solution for nonlocal problems involving
the fractional Laplacian and a critical growth power nonlinearity when the
equation is set in a suitable contractible domain.Comment: 17 page
A note on global regularity for the weak solutions of fractional p-Laplacian equations
We consider a boundary value problem driven by the fractional p-Laplacian
operator with a bounded reaction term. By means of barrier arguments, we prove
H\"older regularity up to the boundary for the weak solutions, both in the
singular (12) case.Comment: 7 pages, Conferenza tenuta al XXV Convegno Nazionale di Calcolo delle
Variazioni, Levico 2--6 febbraio 201