Calculus of Variations and Geometric Measure Theory

K. Bal - K. Mohanta - P. Roy - F. Sk

Hardy and Poincaré inequalities in fractional Orlicz-Sobolev space

created by sk on 21 Nov 2021


Accepted Paper

Inserted: 21 nov 2021

Journal: Nonlinear Analysis
Year: 2021

ArXiv: 2009.07035 PDF


We provide sufficient conditions for boundary Hardy inequality to hold in bounded Lipschitz domains, complement of a point (the so called point Hardy inequality), domain above the graph of a Lipschitz function, complement of a bounded Lipschitz domain in fractional Orlicz-Sobolev setting. As a consequence we get sufficient conditions for regional fractional Orlicz Poincaré inequaliy in bounded Lipschitz domains. Necessary conditions for fractional Orlicz Hardy and regional fractional Orlicz Poincaré inequalities are also given for bounded Lipschitz domains. Various sufficient conditions on open sets are provided for fractional Orlicz Poincaré inequality and regional fractional Orlicz Poincaré inequality to hold.