A Note on Non-Negative Singular Infinity-Harmonic Functions in the Half-Space

In this work we study non-negative singular infinity-harmonic functions in the half-space. We assume that solutions blow-up at the origin while vanishing at infinity and on a hyperplane. We show that blow-up rate is of the order |x|−1/3

Some remarks on the regularity of minimizers of integrals with anisotropic growth

summary:We prove higher integrability for minimizers of some integrals of the calculus of variations; such an improved integrability allows us to get existence of weak second derivatives