alexa On the existence of extremal functions for a weighted Sobolev embedding with critical exponent


Journal of Astrophysics & Aerospace Technology

Author(s): Paolo Caldiroli, Roberta Musina

Abstract Share this page

We investigate the existence of ground state solutions to the Dirichlet problem −÷(|x|α∇u)=|u|2∗α−2u−÷(|x|α∇u)=|u|2α∗−2u in ΩΩ , u = 0 on ∂Ω∂Ω , where α∈(0,2)α∈(0,2) , 2∗α=2nn−2+α2α∗=2nn−2+α and ΩΩ is a domain in RnRn . In particular we prove that a non negative ground state solution exists when the domain ΩΩ is a cone, including the case Ω=RnΩ=Rn . Moroever, we study the case of arbitrary domains, showing how the geometry of the domain near the origin and at infinity affects the existence or non existence of ground state solutions.

This article was published in Calculus of Variations and Partial Differential Equations and referenced in Journal of Astrophysics & Aerospace Technology

Relevant Expert PPTs

Relevant Speaker PPTs

Peer Reviewed Journals
Make the best use of Scientific Research and information from our 700 + peer reviewed, Open Access Journals
International Conferences 2017-18
Meet Inspiring Speakers and Experts at our 3000+ Global Annual Meetings

Contact Us

© 2008-2017 OMICS International - Open Access Publisher. Best viewed in Mozilla Firefox | Google Chrome | Above IE 7.0 version