On fractional Laplacians -- 3

Abstract

We investigate the role of the noncompact group of dilations in ${\mathbb{R}}^n$ on the difference of the quadratic forms associated to the fractional Dirichlet and Navier Laplacians. Then we apply our results to study the Brezis--Nirenberg effect in two families of noncompact boundary value problems involving the Navier-Laplacian.

13 pages

Cited by in corpus (5)

• On the maximum principle for higher-order fractional Laplacians
• A tool for symmetry breaking and multiplicity in some nonlocal problems
• Variational inequalities for the spectral fractional Laplacian
• Dissipative systems fractionally coupled to a bath
• The Lewy-Stampacchia Inequality for the Fractional Laplacian and Its Application to Anomalous Unidirectional Diffusion Equations