A H\"older Infinity Laplacian obtained as limit of Orlicz Fractional Laplacians

Ariel M. Salort; Juli\'an Fern\'andez Bonder; Mayte P\'erez-Llanos

arxiv: 1807.01669 · v1 · pith:HYO7X3ICnew · submitted 2018-07-04 · 🧮 math.AP

A H\"older Infinity Laplacian obtained as limit of Orlicz Fractional Laplacians

Juli\'an Fern\'andez Bonder , Mayte P\'erez-Llanos , Ariel M. Salort This is my paper

classification 🧮 math.AP

keywords fractionallaplacianolderconditionsfamilyfunctioninfinitylimit

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This paper concerns with the study of the asymptotic behavior of the solutions to a family of fractional type problems on a bounded domain, satisfying homogeneous Dirichlet boundary conditions. The family of differential operators includes the fractional $p_n$-Laplacian when $p_n\to\infty$ as a particular case, tough it could be extended to a function of the H\"older quotient of order $s$, whose primitive is an Orlicz function satisfying appropriated growth conditions. The limit equation involves the H\"older infinity Laplacian.

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Asymptotics of Dirichlet Problems to Fractional p-Laplacian Functionals-Approach in De Giorgi Sense
math.AP 2019-07 unverdicted novelty 5.0

Proves Gamma-convergence of non-homogeneous fractional p-Laplacian Dirichlet problems to the Holder infinity-Laplacian as p to infinity and examines asymptotics as k to s from above and below in De Giorgi sense.