arXiv subjects

Maria Agostina Vivaldi

Publications and source records attributed to Maria Agostina Vivaldi.

2 recordsLinked to original sources

arXiv2020

Limit of p-Laplacian Obstacle problems

In this paper we study asymptotic behavior of solutions of obstacle problems for $p-$Laplacians as $p\to \infty.$ For the one-dimensional case and for the radial case, we give an explicit expression of the limit. In the n-dimensional case, we provide sufficient conditions to assure the uniform convergence of whole family of the solutions of obstacle problems either for data $f$ that change sign in $Ω$ or for data $f$ (that do not change sign in $Ω$) possibly vanishing in a set of positive measure.

math.AP↗

arXiv2017

Absolutely Minimizing Lipschitz Extensions and Infinity Harmonic Functions on the Sierpinski gasket

Aim of this note is to study the infinity Laplace operator and the corresponding Absolutely Minimizing Lipschitz Extension problem on the Sierpinski gasket in the spirit of the classical construction of Kigami for the Laplacian. We introduce a notion of infinity harmonic functions on pre-fractal sets and we show that these functions solve a Lipschitz extension problem in the discrete setting. Then we prove that the limit of the infinity harmonic functions on the pre-fractal sets solves the Absolutely Minimizing Lipschitz Extension problem on the Sierpinski gasket.

math.AP↗