descriptionPublicationkeyboard_double_arrow_right Article , Preprint 06 Jun 2016Embargo end date: 01 Jan 2015Publisher:EDP SciencesJournal:ESAIM: Control, Optimisation and Calculus of Variations, volume 22, pages 832-841 (issn: 1292-8119, eissn: 1262-3377,

Authors: MUSINA, Roberta; Nazarov, A. I.;

doi: 10.1051/cocv/2015032 , 10.48550/arxiv.1503.00271

arXiv: 1503.00271

handle: 11390/1071096 , 20.500.11767/32825

On fractional Laplacians – 3

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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

Related Organizations

Department of Mathematical Sciences
Russian Federation
University of Udine
Italy
St. Petersburg Department of Steklov Institute of Mathematics
Russian Federation
International School for Advanced Studies
Italy
Moscow State University of Printing Arts
Russian Federation

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Keywords

Mathematics - Analysis of PDEs, FOS: Mathematics, 47A63, 35A23, Fractional Laplace operators, Navier and Dirichlet boundary conditions, Sobolev in- equality, critical dimensions., Fractional Laplace operators; Navier and Dirichlet boundary conditions; Sobolev in- equality; critical dimensions., Analysis of PDEs (math.AP)

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On fractional Laplacians $– 2$
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