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 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

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

Interactions of the solar neutrinos with the deuterons

Starting from chiral Lagrangians, possessing the SU(2)_L x SU(2)_R local chiral symmetry, we derive weak axial one-boson exchange currents in the leading order in the 1/M expansion (M is the nucleon mass). We apply these currents in calculations of the cross sections for the disintegration of the deuterons by the low energy neutrinos. The nuclear wave functions are derived from a variant of the OBEPQB potential and from the Nijmegen 93 and Nijmegen I nucleon-nucleon interactions. The comparison of our cross sections with those obtained within the pionless effective field theory and other potential model calculations shows that the solar neutrino-deuteron cross sections can be calculated within an accuracy of 3.3 %.Comment: 6 pages, 1 figure, 6 tables, conference tal