Existence and regularity of solutions to semi-linear Dirichlet problem of infinitely degenerate elliptic operators with singular potential term

In this paper, we study the Dirichlet problem for a class of semi-linear infinitely degenerate elliptic equations with singular potential term. By using the logarithmic Sobolev inequality and Hardy＇s inequality, the existence and regularity of multiple nontrivial solutions have been proved.

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Science China. Mathematics 2013-04, Vol.56 (4), p.687-706
Hauptverfasser:	Chen, Hua, Luo, Peng, Tian, ShuYing
Format:	Artikel
Sprache:	eng
Schlagworte:	Applications of Mathematics Astronomy China Dirichlet problem Dirichlet问题 Inequalities Mathematical analysis Mathematics Mathematics and Statistics Operators Regularity Series (mathematics) 半无限半线性奇异对数Sobolev不等式解的存在性退化椭圆算子退缩椭圆型方程
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Beschreibung
Zusammenfassung:	In this paper, we study the Dirichlet problem for a class of semi-linear infinitely degenerate elliptic equations with singular potential term. By using the logarithmic Sobolev inequality and Hardy＇s inequality, the existence and regularity of multiple nontrivial solutions have been proved.
ISSN:	1674-7283 1006-9283 1869-1862
DOI:	10.1007/s11425-013-4588-y