Influence of an lp –perturbation on Hardy-Sobolev inequality with singularity a curve

• Autorzy: Ijaodoro Idowu Esther , Thiam El Hadji Abdoulaye

Identyfikatory

DOI

10.7494/OpMath.2021.41.2.187

• Języki publikacji: EN

Abstrakty

EN

We consider a bounded domain Ω of [formula],[formula] h and b continuous functions on Ω. Let Γ be a closed curve contained in Ω. We study existence of positive solutions [formula] to the perturbed Hardy-Sobolev equation: [formula] where [formula] is the critical Hardy-Sobolev exponent [formula] and [formula] is the distance function to Γ. We show that the existence of minimizers does not depend on the local geometry of Γ nor on the potential h. For N = 3, the existence of ground-state solution may depends on the trace of the regular part of the Green function of —Δ + h and or on b. This is due to the perturbative term of order 1 + δ.

Słowa kluczowe

EN

Hardy-Sobolev inequality; positive minimizers; parametrized curve; mass; Green function

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2021
• Tom: Vol. 41, no. 2
• Strony: 187--204
• Opis fizyczny: Bibliogr, 22 poz.

Twórcy

autor

Ijaodoro Idowu Esther

• African Institute for Mathematical Sciences in Senegal KM 2, Route de Joal, B.P. 14 18, Mbour, Senegal

• https://orcid.org/0000-0002-9550-9090

autor

Thiam El Hadji Abdoulaye

• Universite de Thies UFR des Sciences et Techniques Departement de Mathematiques, Thies, Senegal

• https://orcid.org/0000-0003-1206-8312

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).